Precalculus Examples

$w + 8 z = 0$ , $x + 4 z = 4$ , $y - 7 z = 1$

Step 1

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

$w + 8 z = 0$

$x + 4 z = 4$

Step 2

Eliminate $z$ from the system.

Tap for more steps...

Step 2.1

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

$w + 8 z = 0$

$(- 2) \cdot (x + 4 z) = (- 2) (4)$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Simplify the left side.

Tap for more steps...

Step 2.2.1.1

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

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$w + 8 z = 0$

$- 2 x - 2 (4 z) = (- 2) (4)$

Step 2.2.1.1.2

Multiply $4$ by $- 2$ .

$w + 8 z = 0$

$- 2 x - 8 z = (- 2) (4)$

$w + 8 z = 0$

$- 2 x - 8 z = (- 2) (4)$

$w + 8 z = 0$

$- 2 x - 8 z = (- 2) (4)$

Step 2.2.2

Simplify the right side.

Tap for more steps...

Step 2.2.2.1

Multiply $- 2$ by $4$ .

$w + 8 z = 0$

$- 2 x - 8 z = - 8$

$w + 8 z = 0$

$- 2 x - 8 z = - 8$

$w + 8 z = 0$

$- 2 x - 8 z = - 8$

Step 2.3

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

			$w$	$+$	$8$	$z$	$=$		$0$
		$+$		$-$	$8$	$z$	$=$	$-$	$8$
$-$	$2$	$x$	$w$				$=$	$-$	$8$

Step 2.4

The resultant equation has $z$ eliminated.

$w - 2 x = - 8$

Step 3

Choose another two equations and eliminate $z$ .

$x + 4 z = 4$

$y - 7 z = 1$

Step 4

Eliminate $z$ from the system.

Tap for more steps...

Step 4.1

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

$(7) \cdot (x + 4 z) = (7) (4)$

$(4) \cdot (y - 7 z) = (4) (1)$

Step 4.2

Simplify.

Tap for more steps...

Step 4.2.1

Simplify the left side.

Tap for more steps...

Step 4.2.1.1

Simplify $(7) \cdot (x + 4 z)$ .

Tap for more steps...

Step 4.2.1.1.1

Apply the distributive property.

$7 x + 7 (4 z) = (7) (4)$

$(4) \cdot (y - 7 z) = (4) (1)$

Step 4.2.1.1.2

Multiply $4$ by $7$ .

$7 x + 28 z = (7) (4)$

$(4) \cdot (y - 7 z) = (4) (1)$

$7 x + 28 z = (7) (4)$

$(4) \cdot (y - 7 z) = (4) (1)$

$7 x + 28 z = (7) (4)$

$(4) \cdot (y - 7 z) = (4) (1)$

Step 4.2.2

Simplify the right side.

Tap for more steps...

Step 4.2.2.1

Multiply $7$ by $4$ .

$7 x + 28 z = 28$

$(4) \cdot (y - 7 z) = (4) (1)$

$7 x + 28 z = 28$

$(4) \cdot (y - 7 z) = (4) (1)$

Step 4.2.3

Simplify the left side.

Tap for more steps...

Step 4.2.3.1

Simplify $(4) \cdot (y - 7 z)$ .

Tap for more steps...

Step 4.2.3.1.1

Apply the distributive property.

$7 x + 28 z = 28$

$4 y + 4 (- 7 z) = (4) (1)$

Step 4.2.3.1.2

Multiply $- 7$ by $4$ .

$7 x + 28 z = 28$

$4 y - 28 z = (4) (1)$

$7 x + 28 z = 28$

$4 y - 28 z = (4) (1)$

$7 x + 28 z = 28$

$4 y - 28 z = (4) (1)$

Step 4.2.4

Simplify the right side.

Tap for more steps...

Step 4.2.4.1

Multiply $4$ by $1$ .

$7 x + 28 z = 28$

$4 y - 28 z = 4$

$7 x + 28 z = 28$

$4 y - 28 z = 4$

$7 x + 28 z = 28$

$4 y - 28 z = 4$

Step 4.3

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

		$7$	$x$	$+$	$2$	$8$	$z$	$=$	$2$	$8$
	$+$			$-$	$2$	$8$	$z$	$=$		$4$
$4$	$y$	$7$	$x$	$+$				$=$	$3$	$2$

Step 4.4

The resultant equation has $z$ eliminated.

$7 x + 4 y = 32$

Step 5

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

$w - 2 x = - 8$

$7 x + 4 y = 32$

Step 6

Eliminate $x$ from the system.

Tap for more steps...

Step 6.1

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

$(7) \cdot (w - 2 x) = (7) (- 8)$

$(2) \cdot (7 x + 4 y) = (2) (32)$

Step 6.2

Simplify.

Tap for more steps...

Step 6.2.1

Simplify the left side.

Tap for more steps...

Step 6.2.1.1

Simplify $(7) \cdot (w - 2 x)$ .

Tap for more steps...

Step 6.2.1.1.1

Apply the distributive property.

$7 w + 7 (- 2 x) = (7) (- 8)$

$(2) \cdot (7 x + 4 y) = (2) (32)$

Step 6.2.1.1.2

Multiply $- 2$ by $7$ .

$7 w - 14 x = (7) (- 8)$

$(2) \cdot (7 x + 4 y) = (2) (32)$

$7 w - 14 x = (7) (- 8)$

$(2) \cdot (7 x + 4 y) = (2) (32)$

$7 w - 14 x = (7) (- 8)$

$(2) \cdot (7 x + 4 y) = (2) (32)$

Step 6.2.2

Simplify the right side.

Tap for more steps...

Step 6.2.2.1

Multiply $7$ by $- 8$ .

$7 w - 14 x = - 56$

$(2) \cdot (7 x + 4 y) = (2) (32)$

$7 w - 14 x = - 56$

$(2) \cdot (7 x + 4 y) = (2) (32)$

Step 6.2.3

Simplify the left side.

Tap for more steps...

Step 6.2.3.1

Simplify $(2) \cdot (7 x + 4 y)$ .

Tap for more steps...

Step 6.2.3.1.1

Apply the distributive property.

$7 w - 14 x = - 56$

$2 (7 x) + 2 (4 y) = (2) (32)$

Step 6.2.3.1.2

Multiply.

Tap for more steps...

Step 6.2.3.1.2.1

Multiply $7$ by $2$ .

$7 w - 14 x = - 56$

$14 x + 2 (4 y) = (2) (32)$

Step 6.2.3.1.2.2

Multiply $4$ by $2$ .

$7 w - 14 x = - 56$

$14 x + 8 y = (2) (32)$

$7 w - 14 x = - 56$

$14 x + 8 y = (2) (32)$

$7 w - 14 x = - 56$

$14 x + 8 y = (2) (32)$

$7 w - 14 x = - 56$

$14 x + 8 y = (2) (32)$

Step 6.2.4

Simplify the right side.

Tap for more steps...

Step 6.2.4.1

Multiply $2$ by $32$ .

$7 w - 14 x = - 56$

$14 x + 8 y = 64$

$7 w - 14 x = - 56$

$14 x + 8 y = 64$

$7 w - 14 x = - 56$

$14 x + 8 y = 64$

Step 6.3

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

		$7$	$w$	$-$	$1$	$4$	$x$	$=$	$-$	$5$	$6$
	$+$				$1$	$4$	$x$	$=$		$6$	$4$
$8$	$y$	$7$	$w$	$+$				$=$			$8$

Step 6.4

The resultant equation has $x$ eliminated.

$7 w + 8 y = 8$

Step 6.5

Subtract $8 y$ from both sides of the equation.

$7 w = 8 - 8 y$

Step 6.6

Divide each term in $7 w = 8 - 8 y$ by $7$ and simplify.

Tap for more steps...

Step 6.6.1

Divide each term in $7 w = 8 - 8 y$ by $7$ .

$\frac{7 w}{7} = \frac{8}{7} + \frac{- 8 y}{7}$

Step 6.6.2

Simplify the left side.

Tap for more steps...

Step 6.6.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 6.6.2.1.1

Cancel the common factor.

$\frac{7 w}{7} = \frac{8}{7} + \frac{- 8 y}{7}$

Step 6.6.2.1.2

Divide $w$ by $1$ .

$w = \frac{8}{7} + \frac{- 8 y}{7}$

Step 6.6.3

Simplify the right side.

Tap for more steps...

Step 6.6.3.1

Move the negative in front of the fraction.

$w = \frac{8}{7} - \frac{8 y}{7}$

Step 7

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

Tap for more steps...

Step 7.1

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

$(\frac{8}{7} - \frac{8 y}{7}) - 2 x = - 8$

Step 7.2

Solve for $y$ .

Tap for more steps...

Step 7.2.1

Remove parentheses.

$\frac{8}{7} - \frac{8 y}{7} - 2 x = - 8$

Step 7.2.2

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

Tap for more steps...

Step 7.2.2.1

Subtract $\frac{8}{7}$ from both sides of the equation.

$- \frac{8 y}{7} - 2 x = - 8 - \frac{8}{7}$

Step 7.2.2.2

Add $2 x$ to both sides of the equation.

$- \frac{8 y}{7} = - 8 - \frac{8}{7} + 2 x$

Step 7.2.2.3

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{8 y}{7} = - 8 \cdot \frac{7}{7} - \frac{8}{7} + 2 x$

Step 7.2.2.4

Combine $- 8$ and $\frac{7}{7}$ .

$- \frac{8 y}{7} = \frac{- 8 \cdot 7}{7} - \frac{8}{7} + 2 x$

Step 7.2.2.5

Combine the numerators over the common denominator.

$- \frac{8 y}{7} = \frac{- 8 \cdot 7 - 8}{7} + 2 x$

Step 7.2.2.6

Simplify the numerator.

Tap for more steps...

Step 7.2.2.6.1

Multiply $- 8$ by $7$ .

$- \frac{8 y}{7} = \frac{- 56 - 8}{7} + 2 x$

Step 7.2.2.6.2

Subtract $8$ from $- 56$ .

$- \frac{8 y}{7} = \frac{- 64}{7} + 2 x$

Step 7.2.2.7

Move the negative in front of the fraction.

$- \frac{8 y}{7} = - \frac{64}{7} + 2 x$

Step 7.2.3

Multiply both sides of the equation by $- \frac{7}{8}$ .

$- \frac{7}{8} (- \frac{8 y}{7}) = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4

Simplify both sides of the equation.

Tap for more steps...

Step 7.2.4.1

Simplify the left side.

Tap for more steps...

Step 7.2.4.1.1

Simplify $- \frac{7}{8} (- \frac{8 y}{7})$ .

Tap for more steps...

Step 7.2.4.1.1.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 7.2.4.1.1.1.1

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$\frac{- 7}{8} (- \frac{8 y}{7}) = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.1.2

Move the leading negative in $- \frac{8 y}{7}$ into the numerator.

$\frac{- 7}{8} \cdot \frac{- 8 y}{7} = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{8} \cdot \frac{- 8 y}{7} = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{8} \cdot \frac{- 8 y}{7} = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{8} (- 8 y) = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.2

Cancel the common factor of $8$ .

Tap for more steps...

Step 7.2.4.1.1.2.1

Factor $8$ out of $- 8 y$ .

$\frac{- 1}{8} (8 (- y)) = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{8} (8 (- y)) = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.3

Multiply.

Tap for more steps...

Step 7.2.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{7}{8} (- \frac{64}{7} + 2 x)$

Step 7.2.4.2

Simplify the right side.

Tap for more steps...

Step 7.2.4.2.1

Simplify $- \frac{7}{8} (- \frac{64}{7} + 2 x)$ .

Tap for more steps...

Step 7.2.4.2.1.1

Apply the distributive property.

$y = - \frac{7}{8} (- \frac{64}{7}) - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.2

Cancel the common factor of $7$ .

Tap for more steps...

Step 7.2.4.2.1.2.1

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$y = \frac{- 7}{8} (- \frac{64}{7}) - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.2.2

Move the leading negative in $- \frac{64}{7}$ into the numerator.

$y = \frac{- 7}{8} \cdot \frac{- 64}{7} - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.2.3

Factor $7$ out of $- 7$ .

$y = \frac{7 (- 1)}{8} \cdot \frac{- 64}{7} - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.2.4

Cancel the common factor.

$y = \frac{7 \cdot - 1}{8} \cdot \frac{- 64}{7} - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.2.5

Rewrite the expression.

$y = \frac{- 1}{8} \cdot - 64 - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.3

Cancel the common factor of $8$ .

Tap for more steps...

Step 7.2.4.2.1.3.1

Factor $8$ out of $- 64$ .

$y = \frac{- 1}{8} \cdot (8 (- 8)) - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.3.2

Cancel the common factor.

$y = \frac{- 1}{8} \cdot (8 \cdot - 8) - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.3.3

Rewrite the expression.

$y = - - 8 - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.4

Multiply $- 1$ by $- 8$ .

$y = 8 - \frac{7}{8} (2 x)$

Step 7.2.4.2.1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.2.4.2.1.5.1

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$y = 8 + \frac{- 7}{8} (2 x)$

Step 7.2.4.2.1.5.2

Factor $2$ out of $8$ .

$y = 8 + \frac{- 7}{2 (4)} (2 x)$

Step 7.2.4.2.1.5.3

Factor $2$ out of $2 x$ .

$y = 8 + \frac{- 7}{2 (4)} (2 (x))$

Step 7.2.4.2.1.5.4

Cancel the common factor.

$y = 8 + \frac{- 7}{2 \cdot 4} (2 x)$

Step 7.2.4.2.1.5.5

Rewrite the expression.

$y = 8 + \frac{- 7}{4} x$

Step 7.2.4.2.1.6

Combine $\frac{- 7}{4}$ and $x$ .

$y = 8 + \frac{- 7 x}{4}$

Step 7.2.4.2.1.7

Move the negative in front of the fraction.

$y = 8 - \frac{7 x}{4}$

Step 7.2.5

Reorder $8$ and $- \frac{7 x}{4}$ .

$y = - \frac{7 x}{4} + 8$

Step 8

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

Tap for more steps...

Step 8.1

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

$(\frac{8}{7} - \frac{8 (- \frac{7 x}{4} + 8)}{7}) + 8 z = 0$

Step 8.2

Solve for $x$ .

Tap for more steps...

Step 8.2.1

Simplify $(\frac{8}{7} - \frac{8 (- \frac{7 x}{4} + 8)}{7}) + 8 z$ .

Tap for more steps...

Step 8.2.1.1

Combine the numerators over the common denominator.

$8 z + \frac{8 - 8 (- \frac{7 x}{4} + 8)}{7} = 0$

Step 8.2.1.2

Simplify each term.

Tap for more steps...

Step 8.2.1.2.1

Apply the distributive property.

$8 z + \frac{8 - 8 (- \frac{7 x}{4}) - 8 \cdot 8}{7} = 0$

Step 8.2.1.2.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 8.2.1.2.2.1

Move the leading negative in $- \frac{7 x}{4}$ into the numerator.

$8 z + \frac{8 - 8 \frac{- 7 x}{4} - 8 \cdot 8}{7} = 0$

Step 8.2.1.2.2.2

Factor $4$ out of $- 8$ .

$8 z + \frac{8 + 4 (- 2) \frac{- 7 x}{4} - 8 \cdot 8}{7} = 0$

Step 8.2.1.2.2.3

Cancel the common factor.

$8 z + \frac{8 + 4 \cdot - 2 \frac{- 7 x}{4} - 8 \cdot 8}{7} = 0$

Step 8.2.1.2.2.4

Rewrite the expression.

$8 z + \frac{8 - 2 (- 7 x) - 8 \cdot 8}{7} = 0$

Step 8.2.1.2.3

Multiply $- 7$ by $- 2$ .

$8 z + \frac{8 + 14 x - 8 \cdot 8}{7} = 0$

Step 8.2.1.2.4

Multiply $- 8$ by $8$ .

$8 z + \frac{8 + 14 x - 64}{7} = 0$

Step 8.2.1.3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 8.2.1.3.1

Subtract $64$ from $8$ .

$8 z + \frac{14 x - 56}{7} = 0$

Step 8.2.1.3.2

Cancel the common factor of $14 x - 56$ and $7$ .

Tap for more steps...

Step 8.2.1.3.2.1

Factor $7$ out of $14 x$ .

$8 z + \frac{7 (2 x) - 56}{7} = 0$

Step 8.2.1.3.2.2

Factor $7$ out of $- 56$ .

$8 z + \frac{7 (2 x) + 7 \cdot - 8}{7} = 0$

Step 8.2.1.3.2.3

Factor $7$ out of $7 (2 x) + 7 (- 8)$ .

$8 z + \frac{7 (2 x - 8)}{7} = 0$

Step 8.2.1.3.2.4

Cancel the common factors.

Tap for more steps...

Step 8.2.1.3.2.4.1

Factor $7$ out of $7$ .

$8 z + \frac{7 (2 x - 8)}{7 (1)} = 0$

Step 8.2.1.3.2.4.2

Cancel the common factor.

$8 z + \frac{7 (2 x - 8)}{7 \cdot 1} = 0$

Step 8.2.1.3.2.4.3

Rewrite the expression.

$8 z + \frac{2 x - 8}{1} = 0$

Step 8.2.1.3.2.4.4

Divide $2 x - 8$ by $1$ .

$8 z + 2 x - 8 = 0$

Step 8.2.2

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

Tap for more steps...

Step 8.2.2.1

Subtract $8 z$ from both sides of the equation.

$2 x - 8 = - 8 z$

Step 8.2.2.2

Add $8$ to both sides of the equation.

$2 x = - 8 z + 8$

Step 8.2.3

Divide each term in $2 x = - 8 z + 8$ by $2$ and simplify.

Tap for more steps...

Step 8.2.3.1

Divide each term in $2 x = - 8 z + 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8 z}{2} + \frac{8}{2}$

Step 8.2.3.2

Simplify the left side.

Tap for more steps...

Step 8.2.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8 z}{2} + \frac{8}{2}$

Step 8.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8 z}{2} + \frac{8}{2}$

Step 8.2.3.3

Simplify the right side.

Tap for more steps...

Step 8.2.3.3.1

Simplify each term.

Tap for more steps...

Step 8.2.3.3.1.1

Cancel the common factor of $- 8$ and $2$ .

Tap for more steps...

Step 8.2.3.3.1.1.1

Factor $2$ out of $- 8 z$ .

$x = \frac{2 (- 4 z)}{2} + \frac{8}{2}$

Step 8.2.3.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 8.2.3.3.1.1.2.1

Factor $2$ out of $2$ .

$x = \frac{2 (- 4 z)}{2 (1)} + \frac{8}{2}$

Step 8.2.3.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 (- 4 z)}{2 \cdot 1} + \frac{8}{2}$

Step 8.2.3.3.1.1.2.3

Rewrite the expression.

$x = \frac{- 4 z}{1} + \frac{8}{2}$

Step 8.2.3.3.1.1.2.4

Divide $- 4 z$ by $1$ .

$x = - 4 z + \frac{8}{2}$

Step 8.2.3.3.1.2

Divide $8$ by $2$ .

$x = - 4 z + 4$

Step 9

This is the final solution to the system of equations.

$w = \frac{8}{7} - \frac{8 y}{7}$

$y = - \frac{7 x}{4} + 8$

$x = - 4 z + 4$

			$w$	$+$	$8$	$z$	$=$		$0$
		$+$		$-$	$8$	$z$	$=$	$-$	$8$
$-$	$2$	$x$	$w$				$=$	$-$	$8$

		$7$	$x$	$+$	$2$	$8$	$z$	$=$	$2$	$8$
	$+$			$-$	$2$	$8$	$z$	$=$		$4$
$4$	$y$	$7$	$x$	$+$				$=$	$3$	$2$

		$7$	$w$	$-$	$1$	$4$	$x$	$=$	$-$	$5$	$6$
	$+$				$1$	$4$	$x$	$=$		$6$	$4$
$8$	$y$	$7$	$w$	$+$				$=$			$8$

			$w$	$+$	$8$	$z$	$=$		$0$
		$+$		$-$	$8$	$z$	$=$	$-$	$8$
$-$	$2$	$x$	$w$				$=$	$-$	$8$

		$7$	$x$	$+$	$2$	$8$	$z$	$=$	$2$	$8$
	$+$			$-$	$2$	$8$	$z$	$=$		$4$
$4$	$y$	$7$	$x$	$+$				$=$	$3$	$2$

		$7$	$w$	$-$	$1$	$4$	$x$	$=$	$-$	$5$	$6$
	$+$				$1$	$4$	$x$	$=$		$6$	$4$
$8$	$y$	$7$	$w$	$+$				$=$			$8$

			$w$	$+$	$8$	$z$	$=$		$0$
		$+$		$-$	$8$	$z$	$=$	$-$	$8$
$-$	$2$	$x$	$w$				$=$	$-$	$8$

		$7$	$x$	$+$	$2$	$8$	$z$	$=$	$2$	$8$
	$+$			$-$	$2$	$8$	$z$	$=$		$4$
$4$	$y$	$7$	$x$	$+$				$=$	$3$	$2$

		$7$	$w$	$-$	$1$	$4$	$x$	$=$	$-$	$5$	$6$
	$+$				$1$	$4$	$x$	$=$		$6$	$4$
$8$	$y$	$7$	$w$	$+$				$=$			$8$