Precalculus Examples

$4 (3 x + y) + 2 z = - 1$ , $3 (x - 4 y + 2 z) = 14$ , $9 (- 1 + x) = - 4 (z - 4 y)$

Step 1

Choose two equations and eliminate one variable. In this case, eliminate $z$ .

$4 (3 x + y) + 2 z = - 1$

$3 (x - 4 y + 2 z) = 14$

Step 2

Eliminate $z$ from the system.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$4 (3 x) + 4 y + 2 z = - 1$

$3 (x - 4 y + 2 z) = 14$

Step 2.1.1.2

Multiply $3$ by $4$ .

$12 x + 4 y + 2 z = - 1$

$3 (x - 4 y + 2 z) = 14$

$12 x + 4 y + 2 z = - 1$

$3 (x - 4 y + 2 z) = 14$

$12 x + 4 y + 2 z = - 1$

$3 (x - 4 y + 2 z) = 14$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (x - 4 y + 2 z)$ .

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Step 2.2.1.1

Apply the distributive property.

$3 x + 3 (- 4 y) + 3 (2 z) = 14$

$12 x + 4 y + 2 z = - 1$

Step 2.2.1.2

Simplify.

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Step 2.2.1.2.1

Multiply $- 4$ by $3$ .

$3 x - 12 y + 3 (2 z) = 14$

$12 x + 4 y + 2 z = - 1$

Step 2.2.1.2.2

Multiply $2$ by $3$ .

$3 x - 12 y + 6 z = 14$

$12 x + 4 y + 2 z = - 1$

$3 x - 12 y + 6 z = 14$

$12 x + 4 y + 2 z = - 1$

$3 x - 12 y + 6 z = 14$

$12 x + 4 y + 2 z = - 1$

$3 x - 12 y + 6 z = 14$

$12 x + 4 y + 2 z = - 1$

Step 2.3

Multiply each equation by the value that makes the coefficients of $z$ opposite.

$(- 3) \cdot (12 x + 4 y + 2 z) = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

Step 2.4

Simplify.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $(- 3) \cdot (12 x + 4 y + 2 z)$ .

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Step 2.4.1.1.1

Apply the distributive property.

$- 3 (12 x) - 3 (4 y) - 3 (2 z) = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $12$ by $- 3$ .

$- 36 x - 3 (4 y) - 3 (2 z) = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

Step 2.4.1.1.2.2

Multiply $4$ by $- 3$ .

$- 36 x - 12 y - 3 (2 z) = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

Step 2.4.1.1.2.3

Multiply $2$ by $- 3$ .

$- 36 x - 12 y - 6 z = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

$- 36 x - 12 y - 6 z = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

$- 36 x - 12 y - 6 z = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

$- 36 x - 12 y - 6 z = (- 3) (- 1)$

$3 x - 12 y + 6 z = 14$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Multiply $- 3$ by $- 1$ .

$- 36 x - 12 y - 6 z = 3$

$3 x - 12 y + 6 z = 14$

$- 36 x - 12 y - 6 z = 3$

$3 x - 12 y + 6 z = 14$

$- 36 x - 12 y - 6 z = 3$

$3 x - 12 y + 6 z = 14$

Step 2.5

Add the two equations together to eliminate $z$ from the system.

	$-$	$3$	$6$	$x$	$-$	$1$	$2$	$y$	$-$	$6$	$z$	$=$		$3$
$+$			$3$	$x$	$-$	$1$	$2$	$y$	$+$	$6$	$z$	$=$	$1$	$4$
	$-$	$3$	$3$	$x$	$-$	$2$	$4$	$y$				$=$	$1$	$7$

Step 2.6

The resultant equation has $z$ eliminated.

$- 33 x - 24 y = 17$

Step 3

Choose another two equations and eliminate $z$ .

$3 (x - 4 y + 2 z) = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

Step 4

Eliminate $z$ from the system.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $3 (x - 4 y + 2 z)$ .

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Step 4.1.1.1

Apply the distributive property.

$3 x + 3 (- 4 y) + 3 (2 z) = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

Step 4.1.1.2

Simplify.

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Step 4.1.1.2.1

Multiply $- 4$ by $3$ .

$3 x - 12 y + 3 (2 z) = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

Step 4.1.1.2.2

Multiply $2$ by $3$ .

$3 x - 12 y + 6 z = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

$9 (- 1 + x) = - 4 (z - 4 y)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $9 (- 1 + x)$ .

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Step 4.2.1.1

Apply the distributive property.

$9 \cdot - 1 + 9 x = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $9$ by $- 1$ .

$- 9 + 9 x = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

Step 4.2.1.2.2

Reorder $- 9$ and $9 x$ .

$9 x - 9 = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

$9 x - 9 = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

$9 x - 9 = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

$9 x - 9 = - 4 (z - 4 y)$

$3 x - 12 y + 6 z = 14$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify $- 4 (z - 4 y)$ .

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Step 4.3.1.1

Apply the distributive property.

$9 x - 9 = - 4 z - 4 (- 4 y)$

$3 x - 12 y + 6 z = 14$

Step 4.3.1.2

Simplify the expression.

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Step 4.3.1.2.1

Multiply $- 4$ by $- 4$ .

$9 x - 9 = - 4 z + 16 y$

$3 x - 12 y + 6 z = 14$

Step 4.3.1.2.2

Reorder $- 4 z$ and $16 y$ .

$9 x - 9 = 16 y - 4 z$

$3 x - 12 y + 6 z = 14$

$9 x - 9 = 16 y - 4 z$

$3 x - 12 y + 6 z = 14$

$9 x - 9 = 16 y - 4 z$

$3 x - 12 y + 6 z = 14$

$9 x - 9 = 16 y - 4 z$

$3 x - 12 y + 6 z = 14$

Step 4.4

Move all terms containing variables to the left.

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Step 4.4.1

Add $9$ to both sides of the equation.

$3 x - 12 y + 6 z = 14, 9 x = 16 y - 4 z + 9$

Step 4.4.2

Move all terms containing variables to the left side of the equation.

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Step 4.4.2.1

Subtract $16 y$ from both sides of the equation.

$3 x - 12 y + 6 z = 14, 9 x - 16 y = - 4 z + 9$

Step 4.4.2.2

Add $4 z$ to both sides of the equation.

$3 x - 12 y + 6 z = 14, 9 x - 16 y + 4 z = 9$

Step 4.5

Multiply each equation by the value that makes the coefficients of $z$ opposite.

$(- 2) \cdot (3 x - 12 y + 6 z) = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

Step 4.6

Simplify.

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Step 4.6.1

Simplify the left side.

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Step 4.6.1.1

Simplify $(- 2) \cdot (3 x - 12 y + 6 z)$ .

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Step 4.6.1.1.1

Apply the distributive property.

$- 2 (3 x) - 2 (- 12 y) - 2 (6 z) = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

Step 4.6.1.1.2

Simplify.

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Step 4.6.1.1.2.1

Multiply $3$ by $- 2$ .

$- 6 x - 2 (- 12 y) - 2 (6 z) = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

Step 4.6.1.1.2.2

Multiply $- 12$ by $- 2$ .

$- 6 x + 24 y - 2 (6 z) = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

Step 4.6.1.1.2.3

Multiply $6$ by $- 2$ .

$- 6 x + 24 y - 12 z = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

$- 6 x + 24 y - 12 z = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

$- 6 x + 24 y - 12 z = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

$- 6 x + 24 y - 12 z = (- 2) (14)$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

Step 4.6.2

Simplify the right side.

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Step 4.6.2.1

Multiply $- 2$ by $14$ .

$- 6 x + 24 y - 12 z = - 28$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

$- 6 x + 24 y - 12 z = - 28$

$(3) \cdot (9 x - 16 y + 4 z) = (3) (9)$

Step 4.6.3

Simplify the left side.

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Step 4.6.3.1

Simplify $(3) \cdot (9 x - 16 y + 4 z)$ .

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Step 4.6.3.1.1

Apply the distributive property.

$- 6 x + 24 y - 12 z = - 28$

$3 (9 x) + 3 (- 16 y) + 3 (4 z) = (3) (9)$

Step 4.6.3.1.2

Simplify.

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Step 4.6.3.1.2.1

Multiply $9$ by $3$ .

$- 6 x + 24 y - 12 z = - 28$

$27 x + 3 (- 16 y) + 3 (4 z) = (3) (9)$

Step 4.6.3.1.2.2

Multiply $- 16$ by $3$ .

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 3 (4 z) = (3) (9)$

Step 4.6.3.1.2.3

Multiply $4$ by $3$ .

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = (3) (9)$

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = (3) (9)$

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = (3) (9)$

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = (3) (9)$

Step 4.6.4

Simplify the right side.

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Step 4.6.4.1

Multiply $3$ by $9$ .

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = 27$

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = 27$

$- 6 x + 24 y - 12 z = - 28$

$27 x - 48 y + 12 z = 27$

Step 4.7

Add the two equations together to eliminate $z$ from the system.

	$-$	$6$	$x$	$+$	$2$	$4$	$y$	$-$	$1$	$2$	$z$	$=$	$-$	$2$	$8$
$+$	$2$	$7$	$x$	$-$	$4$	$8$	$y$	$+$	$1$	$2$	$z$	$=$		$2$	$7$
	$2$	$1$	$x$	$-$	$2$	$4$	$y$					$=$		$-$	$1$

Step 4.8

The resultant equation has $z$ eliminated.

$21 x - 24 y = - 1$

Step 5

Take the resultant equations and eliminate another variable. In this case, eliminate $y$ .

$- 33 x - 24 y = 17$

$21 x - 24 y = - 1$

Step 6

Eliminate $y$ from the system.

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Step 6.1

Multiply each equation by the value that makes the coefficients of $y$ opposite.

$(- 1) \cdot (- 33 x - 24 y) = (- 1) (17)$

$21 x - 24 y = - 1$

Step 6.2

Simplify.

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Step 6.2.1

Simplify the left side.

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Step 6.2.1.1

Simplify $(- 1) \cdot (- 33 x - 24 y)$ .

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Step 6.2.1.1.1

Apply the distributive property.

$- 1 (- 33 x) - 1 (- 24 y) = (- 1) (17)$

$21 x - 24 y = - 1$

Step 6.2.1.1.2

Multiply.

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Step 6.2.1.1.2.1

Multiply $- 33$ by $- 1$ .

$33 x - 1 (- 24 y) = (- 1) (17)$

$21 x - 24 y = - 1$

Step 6.2.1.1.2.2

Multiply $- 24$ by $- 1$ .

$33 x + 24 y = (- 1) (17)$

$21 x - 24 y = - 1$

$33 x + 24 y = (- 1) (17)$

$21 x - 24 y = - 1$

$33 x + 24 y = (- 1) (17)$

$21 x - 24 y = - 1$

$33 x + 24 y = (- 1) (17)$

$21 x - 24 y = - 1$

Step 6.2.2

Simplify the right side.

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Step 6.2.2.1

Multiply $- 1$ by $17$ .

$33 x + 24 y = - 17$

$21 x - 24 y = - 1$

$33 x + 24 y = - 17$

$21 x - 24 y = - 1$

$33 x + 24 y = - 17$

$21 x - 24 y = - 1$

Step 6.3

Add the two equations together to eliminate $y$ from the system.

	$3$	$3$	$x$	$+$	$2$	$4$	$y$	$=$	$-$	$1$	$7$
$+$	$2$	$1$	$x$	$-$	$2$	$4$	$y$	$=$		$-$	$1$
	$5$	$4$	$x$					$=$	$-$	$1$	$8$

Step 6.4

The resultant equation has $y$ eliminated.

$54 x = - 18$

Step 6.5

Divide each term in $54 x = - 18$ by $54$ and simplify.

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Step 6.5.1

Divide each term in $54 x = - 18$ by $54$ .

$\frac{54 x}{54} = \frac{- 18}{54}$

Step 6.5.2

Simplify the left side.

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Step 6.5.2.1

Cancel the common factor of $54$ .

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Step 6.5.2.1.1

Cancel the common factor.

$\frac{54 x}{54} = \frac{- 18}{54}$

Step 6.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 18}{54}$

Step 6.5.3

Simplify the right side.

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Step 6.5.3.1

Cancel the common factor of $- 18$ and $54$ .

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Step 6.5.3.1.1

Factor $18$ out of $- 18$ .

$x = \frac{18 (- 1)}{54}$

Step 6.5.3.1.2

Cancel the common factors.

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Step 6.5.3.1.2.1

Factor $18$ out of $54$ .

$x = \frac{18 \cdot - 1}{18 \cdot 3}$

Step 6.5.3.1.2.2

Cancel the common factor.

$x = \frac{18 \cdot - 1}{18 \cdot 3}$

Step 6.5.3.1.2.3

Rewrite the expression.

$x = \frac{- 1}{3}$

Step 6.5.3.2

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Step 7

Substitute the value of $x$ into an equation with $z$ eliminated already and solve for the remaining variable.

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Step 7.1

Substitute the value of $x$ into an equation with $z$ eliminated already.

$- 33 (- \frac{1}{3}) - 24 y = 17$

Step 7.2

Solve for $y$ .

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Step 7.2.1

Simplify each term.

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Step 7.2.1.1

Cancel the common factor of $3$ .

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Step 7.2.1.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$- 33 (\frac{- 1}{3}) - 24 y = 17$

Step 7.2.1.1.2

Factor $3$ out of $- 33$ .

$3 (- 11) \frac{- 1}{3} - 24 y = 17$

Step 7.2.1.1.3

Cancel the common factor.

$3 \cdot - 11 \frac{- 1}{3} - 24 y = 17$

Step 7.2.1.1.4

Rewrite the expression.

$- 11 \cdot - 1 - 24 y = 17$

Step 7.2.1.2

Multiply $- 11$ by $- 1$ .

$11 - 24 y = 17$

Step 7.2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 7.2.2.1

Subtract $11$ from both sides of the equation.

$- 24 y = 17 - 11$

Step 7.2.2.2

Subtract $11$ from $17$ .

$- 24 y = 6$

Step 7.2.3

Divide each term in $- 24 y = 6$ by $- 24$ and simplify.

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Step 7.2.3.1

Divide each term in $- 24 y = 6$ by $- 24$ .

$\frac{- 24 y}{- 24} = \frac{6}{- 24}$

Step 7.2.3.2

Simplify the left side.

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Step 7.2.3.2.1

Cancel the common factor of $- 24$ .

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Step 7.2.3.2.1.1

Cancel the common factor.

$\frac{- 24 y}{- 24} = \frac{6}{- 24}$

Step 7.2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{- 24}$

Step 7.2.3.3

Simplify the right side.

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Step 7.2.3.3.1

Cancel the common factor of $6$ and $- 24$ .

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Step 7.2.3.3.1.1

Factor $6$ out of $6$ .

$y = \frac{6 (1)}{- 24}$

Step 7.2.3.3.1.2

Cancel the common factors.

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Step 7.2.3.3.1.2.1

Factor $6$ out of $- 24$ .

$y = \frac{6 \cdot 1}{6 \cdot - 4}$

Step 7.2.3.3.1.2.2

Cancel the common factor.

$y = \frac{6 \cdot 1}{6 \cdot - 4}$

Step 7.2.3.3.1.2.3

Rewrite the expression.

$y = \frac{1}{- 4}$

Step 7.2.3.3.2

Move the negative in front of the fraction.

$y = - \frac{1}{4}$

Step 8

Substitute the value of each known variable into one of the initial equations and solve for the last variable.

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Step 8.1

Substitute the value of each known variable into one of the initial equations.

$4 (3 (- \frac{1}{3}) - \frac{1}{4}) + 2 z = - 1$

Step 8.2

Solve for $z$ .

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Step 8.2.1

Simplify each term.

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Step 8.2.1.1

Cancel the common factor of $3$ .

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Step 8.2.1.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$4 (3 (\frac{- 1}{3}) - \frac{1}{4}) + 2 z = - 1$

Step 8.2.1.1.2

Cancel the common factor.

$4 (3 (\frac{- 1}{3}) - \frac{1}{4}) + 2 z = - 1$

Step 8.2.1.1.3

Rewrite the expression.

$4 (- 1 - \frac{1}{4}) + 2 z = - 1$

Step 8.2.1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 (- 1 \cdot \frac{4}{4} - \frac{1}{4}) + 2 z = - 1$

Step 8.2.1.3

Combine $- 1$ and $\frac{4}{4}$ .

$4 (\frac{- 1 \cdot 4}{4} - \frac{1}{4}) + 2 z = - 1$

Step 8.2.1.4

Combine the numerators over the common denominator.

$4 \frac{- 1 \cdot 4 - 1}{4} + 2 z = - 1$

Step 8.2.1.5

Simplify the numerator.

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Step 8.2.1.5.1

Multiply $- 1$ by $4$ .

$4 \frac{- 4 - 1}{4} + 2 z = - 1$

Step 8.2.1.5.2

Subtract $1$ from $- 4$ .

$4 (\frac{- 5}{4}) + 2 z = - 1$

Step 8.2.1.6

Cancel the common factor of $4$ .

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Step 8.2.1.6.1

Cancel the common factor.

$4 (\frac{- 5}{4}) + 2 z = - 1$

Step 8.2.1.6.2

Rewrite the expression.

$- 5 + 2 z = - 1$

Step 8.2.2

Move all terms not containing $z$ to the right side of the equation.

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Step 8.2.2.1

Add $5$ to both sides of the equation.

$2 z = - 1 + 5$

Step 8.2.2.2

Add $- 1$ and $5$ .

$2 z = 4$

Step 8.2.3

Divide each term in $2 z = 4$ by $2$ and simplify.

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Step 8.2.3.1

Divide each term in $2 z = 4$ by $2$ .

$\frac{2 z}{2} = \frac{4}{2}$

Step 8.2.3.2

Simplify the left side.

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Step 8.2.3.2.1

Cancel the common factor of $2$ .

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Step 8.2.3.2.1.1

Cancel the common factor.

$\frac{2 z}{2} = \frac{4}{2}$

Step 8.2.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{4}{2}$

Step 8.2.3.3

Simplify the right side.

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Step 8.2.3.3.1

Divide $4$ by $2$ .

$z = 2$

Step 9

The solution to the system of equations can be represented as a point.

$(- \frac{1}{3}, - \frac{1}{4}, 2)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{3}, - \frac{1}{4}, 2)$

Equation Form:

$x = - \frac{1}{3}, y = - \frac{1}{4}, z = 2$

	$-$	$3$	$6$	$x$	$-$	$1$	$2$	$y$	$-$	$6$	$z$	$=$		$3$
$+$			$3$	$x$	$-$	$1$	$2$	$y$	$+$	$6$	$z$	$=$	$1$	$4$
	$-$	$3$	$3$	$x$	$-$	$2$	$4$	$y$				$=$	$1$	$7$

	$-$	$6$	$x$	$+$	$2$	$4$	$y$	$-$	$1$	$2$	$z$	$=$	$-$	$2$	$8$
$+$	$2$	$7$	$x$	$-$	$4$	$8$	$y$	$+$	$1$	$2$	$z$	$=$		$2$	$7$
	$2$	$1$	$x$	$-$	$2$	$4$	$y$					$=$		$-$	$1$

	$3$	$3$	$x$	$+$	$2$	$4$	$y$	$=$	$-$	$1$	$7$
$+$	$2$	$1$	$x$	$-$	$2$	$4$	$y$	$=$		$-$	$1$
	$5$	$4$	$x$					$=$	$-$	$1$	$8$

	$-$	$3$	$6$	$x$	$-$	$1$	$2$	$y$	$-$	$6$	$z$	$=$		$3$
$+$			$3$	$x$	$-$	$1$	$2$	$y$	$+$	$6$	$z$	$=$	$1$	$4$
	$-$	$3$	$3$	$x$	$-$	$2$	$4$	$y$				$=$	$1$	$7$

	$-$	$6$	$x$	$+$	$2$	$4$	$y$	$-$	$1$	$2$	$z$	$=$	$-$	$2$	$8$
$+$	$2$	$7$	$x$	$-$	$4$	$8$	$y$	$+$	$1$	$2$	$z$	$=$		$2$	$7$
	$2$	$1$	$x$	$-$	$2$	$4$	$y$					$=$		$-$	$1$

	$3$	$3$	$x$	$+$	$2$	$4$	$y$	$=$	$-$	$1$	$7$
$+$	$2$	$1$	$x$	$-$	$2$	$4$	$y$	$=$		$-$	$1$
	$5$	$4$	$x$					$=$	$-$	$1$	$8$

	$-$	$3$	$6$	$x$	$-$	$1$	$2$	$y$	$-$	$6$	$z$	$=$		$3$
$+$			$3$	$x$	$-$	$1$	$2$	$y$	$+$	$6$	$z$	$=$	$1$	$4$
	$-$	$3$	$3$	$x$	$-$	$2$	$4$	$y$				$=$	$1$	$7$

	$-$	$6$	$x$	$+$	$2$	$4$	$y$	$-$	$1$	$2$	$z$	$=$	$-$	$2$	$8$
$+$	$2$	$7$	$x$	$-$	$4$	$8$	$y$	$+$	$1$	$2$	$z$	$=$		$2$	$7$
	$2$	$1$	$x$	$-$	$2$	$4$	$y$					$=$		$-$	$1$

	$3$	$3$	$x$	$+$	$2$	$4$	$y$	$=$	$-$	$1$	$7$
$+$	$2$	$1$	$x$	$-$	$2$	$4$	$y$	$=$		$-$	$1$
	$5$	$4$	$x$					$=$	$-$	$1$	$8$