Solve by Addition/Elimination -4x+9y=-17 3x-4y=10

$- 4 x + 9 y = - 17$ $3 x - 4 y = 10$

Step 1

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

$(3) \cdot (- 4 x + 9 y) = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$3 (- 4 x) + 3 (9 y) = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

Multiply.

Multiply $- 4$ by $3$ .

$- 12 x + 3 (9 y) = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

Multiply $9$ by $3$ .

$- 12 x + 27 y = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

$- 12 x + 27 y = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

$- 12 x + 27 y = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

$- 12 x + 27 y = (3) (- 17)$

$(4) \cdot (3 x - 4 y) = (4) (10)$

Simplify the right side.

Multiply $3$ by $- 17$ .

$- 12 x + 27 y = - 51$

$(4) \cdot (3 x - 4 y) = (4) (10)$

$- 12 x + 27 y = - 51$

$(4) \cdot (3 x - 4 y) = (4) (10)$

Simplify the left side.

Simplify $(4) \cdot (3 x - 4 y)$ .

Apply the distributive property.

$- 12 x + 27 y = - 51$

$4 (3 x) + 4 (- 4 y) = (4) (10)$

Multiply.

Multiply $3$ by $4$ .

$- 12 x + 27 y = - 51$

$12 x + 4 (- 4 y) = (4) (10)$

Multiply $- 4$ by $4$ .

$- 12 x + 27 y = - 51$

$12 x - 16 y = (4) (10)$

$- 12 x + 27 y = - 51$

$12 x - 16 y = (4) (10)$

$- 12 x + 27 y = - 51$

$12 x - 16 y = (4) (10)$

$- 12 x + 27 y = - 51$

$12 x - 16 y = (4) (10)$

Simplify the right side.

Multiply $4$ by $10$ .

$- 12 x + 27 y = - 51$

$12 x - 16 y = 40$

$- 12 x + 27 y = - 51$

$12 x - 16 y = 40$

$- 12 x + 27 y = - 51$

$12 x - 16 y = 40$

Step 3

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

	$-$	$1$	$2$	$x$	$+$	$2$	$7$	$y$	$=$	$-$	$5$	$1$
$+$		$1$	$2$	$x$	$-$	$1$	$6$	$y$	$=$		$4$	$0$
						$1$	$1$	$y$	$=$	$-$	$1$	$1$

Step 4

Divide each term in $11 y = - 11$ by $11$ and simplify.

Divide each term in $11 y = - 11$ by $11$ .

$\frac{11 y}{11} = \frac{- 11}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{- 11}{11}$

Divide $y$ by $1$ .

$y = \frac{- 11}{11}$

Simplify the right side.

Divide $- 11$ by $11$ .

$y = - 1$

Step 5

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 $x$ .

$- 12 x + 27 (- 1) = - 51$

Multiply $27$ by $- 1$ .

$- 12 x - 27 = - 51$

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

Add $27$ to both sides of the equation.

$- 12 x = - 51 + 27$

Add $- 51$ and $27$ .

$- 12 x = - 24$

Divide each term in $- 12 x = - 24$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 24$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 24}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 24}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 12}$

Simplify the right side.

Divide $- 24$ by $- 12$ .

$x = 2$

Step 6

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

$(2, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 8

Solve by Addition/Elimination -4x+9y=-17 3x-4y=10

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