Algebra Examples

$y = 6 x - 11$ $- 2 x - 3 y = - 7$

Step 1

Subtract $6 x$ from both sides of the equation.

$y - 6 x = - 11, - 2 x - 3 y = - 7$

Step 2

Reorder the polynomial.

$- 6 x + y = - 11$

$- 2 x - 3 y = - 7$

Step 3

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

$(3) \cdot (- 6 x + y) = (3) (- 11)$

$- 2 x - 3 y = - 7$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Apply the distributive property.

$3 (- 6 x) + 3 y = (3) (- 11)$

$- 2 x - 3 y = - 7$

Step 4.1.1.2

Multiply $- 6$ by $3$ .

$- 18 x + 3 y = (3) (- 11)$

$- 2 x - 3 y = - 7$

$- 18 x + 3 y = (3) (- 11)$

$- 2 x - 3 y = - 7$

$- 18 x + 3 y = (3) (- 11)$

$- 2 x - 3 y = - 7$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $3$ by $- 11$ .

$- 18 x + 3 y = - 33$

$- 2 x - 3 y = - 7$

$- 18 x + 3 y = - 33$

$- 2 x - 3 y = - 7$

$- 18 x + 3 y = - 33$

$- 2 x - 3 y = - 7$

Step 5

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

	$-$	$1$	$8$	$x$	$+$	$3$	$y$	$=$	$-$	$3$	$3$
$+$		$-$	$2$	$x$	$-$	$3$	$y$	$=$		$-$	$7$
	$-$	$2$	$0$	$x$				$=$	$-$	$4$	$0$

Step 6

Divide each term in $- 20 x = - 40$ by $- 20$ and simplify.

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Step 6.1

Divide each term in $- 20 x = - 40$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 40}{- 20}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 20$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 40}{- 20}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 40}{- 20}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 40$ by $- 20$ .

$x = 2$

Step 7

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

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Step 7.1

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$- 18 \cdot 2 + 3 y = - 33$

Step 7.2

Multiply $- 18$ by $2$ .

$- 36 + 3 y = - 33$

Step 7.3

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

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Step 7.3.1

Add $36$ to both sides of the equation.

$3 y = - 33 + 36$

Step 7.3.2

Add $- 33$ and $36$ .

$3 y = 3$

Step 7.4

Divide each term in $3 y = 3$ by $3$ and simplify.

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Step 7.4.1

Divide each term in $3 y = 3$ by $3$ .

$\frac{3 y}{3} = \frac{3}{3}$

Step 7.4.2

Simplify the left side.

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Step 7.4.2.1

Cancel the common factor of $3$ .

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Step 7.4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{3}{3}$

Step 7.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{3}{3}$

Step 7.4.3

Simplify the right side.

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Step 7.4.3.1

Divide $3$ by $3$ .

$y = 1$

Step 8

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

$(2, 1)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 10

	$-$	$1$	$8$	$x$	$+$	$3$	$y$	$=$	$-$	$3$	$3$
$+$		$-$	$2$	$x$	$-$	$3$	$y$	$=$		$-$	$7$
	$-$	$2$	$0$	$x$				$=$	$-$	$4$	$0$

	$-$	$1$	$8$	$x$	$+$	$3$	$y$	$=$	$-$	$3$	$3$
$+$		$-$	$2$	$x$	$-$	$3$	$y$	$=$		$-$	$7$
	$-$	$2$	$0$	$x$				$=$	$-$	$4$	$0$

	$-$	$1$	$8$	$x$	$+$	$3$	$y$	$=$	$-$	$3$	$3$
$+$		$-$	$2$	$x$	$-$	$3$	$y$	$=$		$-$	$7$
	$-$	$2$	$0$	$x$				$=$	$-$	$4$	$0$