Solve by Addition/Elimination 6x-6y+11=17 9y=3x+15

$6 x - 6 y + 11 = 17$ $9 y = 3 x + 15$

Step 1

Move all terms containing variables to the left.

Subtract $11$ from both sides of the equation.

$6 x - 6 y = 17 - 11, 9 y = 3 x + 15$

Subtract $11$ from $17$ .

$6 x - 6 y = 6, 9 y = 3 x + 15$

Subtract $3 x$ from both sides of the equation.

$6 x - 6 y = 6, 9 y - 3 x = 15$

Step 2

Reorder the polynomial.

$- 3 x + 9 y = 15$

$6 x - 6 y = 6$

Step 3

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

$6 x - 6 y = 6$

$(2) \cdot (- 3 x + 9 y) = (2) (15)$

Step 4

Simplify.

Simplify the left side.

Simplify $(2) \cdot (- 3 x + 9 y)$ .

Apply the distributive property.

$6 x - 6 y = 6$

$2 (- 3 x) + 2 (9 y) = (2) (15)$

Multiply.

Multiply $- 3$ by $2$ .

$6 x - 6 y = 6$

$- 6 x + 2 (9 y) = (2) (15)$

Multiply $9$ by $2$ .

$6 x - 6 y = 6$

$- 6 x + 18 y = (2) (15)$

$6 x - 6 y = 6$

$- 6 x + 18 y = (2) (15)$

$6 x - 6 y = 6$

$- 6 x + 18 y = (2) (15)$

$6 x - 6 y = 6$

$- 6 x + 18 y = (2) (15)$

Simplify the right side.

Multiply $2$ by $15$ .

$6 x - 6 y = 6$

$- 6 x + 18 y = 30$

$6 x - 6 y = 6$

$- 6 x + 18 y = 30$

$6 x - 6 y = 6$

$- 6 x + 18 y = 30$

Step 5

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

		$6$	$x$		$-$	$6$	$y$	$=$		$6$
$+$	$-$	$6$	$x$	$+$	$1$	$8$	$y$	$=$	$3$	$0$
					$1$	$2$	$y$	$=$	$3$	$6$

Step 6

Divide each term in $12 y = 36$ by $12$ and simplify.

Divide each term in $12 y = 36$ by $12$ .

$\frac{12 y}{12} = \frac{36}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 y}{12} = \frac{36}{12}$

Divide $y$ by $1$ .

$y = \frac{36}{12}$

Simplify the right side.

Divide $36$ by $12$ .

$y = 3$

Step 7

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

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

$6 x - 6 \cdot 3 = 6$

Multiply $- 6$ by $3$ .

$6 x - 18 = 6$

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

Add $18$ to both sides of the equation.

$6 x = 6 + 18$

Add $6$ and $18$ .

$6 x = 24$

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

Divide each term in $6 x = 24$ by $6$ .

$\frac{6 x}{6} = \frac{24}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{24}{6}$

Divide $x$ by $1$ .

$x = \frac{24}{6}$

Simplify the right side.

Divide $24$ by $6$ .

$x = 4$

Step 8

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

$(4, 3)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(4, 3)$

Equation Form:

$x = 4, y = 3$

Step 10

Solve by Addition/Elimination 6x-6y+11=17 9y=3x+15

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