Solve by Addition/Elimination -9y+4x-11=0 -3y+10x+31=0

$- 9 y + 4 x - 11 = 0$ $- 3 y + 10 x + 31 = 0$

Step 1

Simplify the left side.

Reorder $- 9 y$ and $4 x$ .

$4 x - 9 y - 11 = 0$

$- 3 y + 10 x + 31 = 0$

$4 x - 9 y - 11 = 0$

$- 3 y + 10 x + 31 = 0$

Step 2

Simplify the left side.

Reorder $- 3 y$ and $10 x$ .

$10 x - 3 y + 31 = 0$

$4 x - 9 y - 11 = 0$

$10 x - 3 y + 31 = 0$

$4 x - 9 y - 11 = 0$

Step 3

Add $11$ to both sides of the equation.

$4 x - 9 y = 11$

$10 x - 3 y + 31 = 0$

Step 4

Subtract $31$ from both sides of the equation.

$10 x - 3 y = - 31$

$4 x - 9 y = 11$

Step 5

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

$4 x - 9 y = 11$

$(- 3) \cdot (10 x - 3 y) = (- 3) (- 31)$

Step 6

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (10 x - 3 y)$ .

Apply the distributive property.

$4 x - 9 y = 11$

$- 3 (10 x) - 3 (- 3 y) = (- 3) (- 31)$

Multiply.

Multiply $10$ by $- 3$ .

$4 x - 9 y = 11$

$- 30 x - 3 (- 3 y) = (- 3) (- 31)$

Multiply $- 3$ by $- 3$ .

$4 x - 9 y = 11$

$- 30 x + 9 y = (- 3) (- 31)$

$4 x - 9 y = 11$

$- 30 x + 9 y = (- 3) (- 31)$

$4 x - 9 y = 11$

$- 30 x + 9 y = (- 3) (- 31)$

$4 x - 9 y = 11$

$- 30 x + 9 y = (- 3) (- 31)$

Simplify the right side.

Multiply $- 3$ by $- 31$ .

$4 x - 9 y = 11$

$- 30 x + 9 y = 93$

$4 x - 9 y = 11$

$- 30 x + 9 y = 93$

$4 x - 9 y = 11$

$- 30 x + 9 y = 93$

Step 7

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

			$4$	$x$	$-$	$9$	$y$	$=$	$1$	$1$
$+$	$-$	$3$	$0$	$x$	$+$	$9$	$y$	$=$	$9$	$3$
	$-$	$2$	$6$	$x$				$=$	$1$	$0$	$4$

Step 8

Divide each term in $- 26 x = 104$ by $- 26$ and simplify.

Divide each term in $- 26 x = 104$ by $- 26$ .

$\frac{- 26 x}{- 26} = \frac{104}{- 26}$

Simplify the left side.

Cancel the common factor of $- 26$ .

Cancel the common factor.

$\frac{- 26 x}{- 26} = \frac{104}{- 26}$

Divide $x$ by $1$ .

$x = \frac{104}{- 26}$

Simplify the right side.

Divide $104$ by $- 26$ .

$x = - 4$

Step 9

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

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

$4 (- 4) - 9 y = 11$

Multiply $4$ by $- 4$ .

$- 16 - 9 y = 11$

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

Add $16$ to both sides of the equation.

$- 9 y = 11 + 16$

Add $11$ and $16$ .

$- 9 y = 27$

Divide each term in $- 9 y = 27$ by $- 9$ and simplify.

Divide each term in $- 9 y = 27$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{27}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{27}{- 9}$

Divide $y$ by $1$ .

$y = \frac{27}{- 9}$

Simplify the right side.

Divide $27$ by $- 9$ .

$y = - 3$

Step 10

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

$(- 4, - 3)$

Step 11

The result can be shown in multiple forms.

Point Form:

$(- 4, - 3)$

Equation Form:

$x = - 4, y = - 3$

Step 12

Solve by Addition/Elimination -9y+4x-11=0 -3y+10x+31=0

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