Solve by Addition/Elimination 5x-6y=-25 , 4x-3y+20=0

$5 x - 6 y = - 25$ , $4 x - 3 y + 20 = 0$

Step 1

Subtract $20$ from both sides of the equation.

$4 x - 3 y = - 20$

$5 x - 6 y = - 25$

Step 2

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

$5 x - 6 y = - 25$

$(- 2) \cdot (4 x - 3 y) = (- 2) (- 20)$

Step 3

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (4 x - 3 y)$ .

Apply the distributive property.

$5 x - 6 y = - 25$

$- 2 (4 x) - 2 (- 3 y) = (- 2) (- 20)$

Multiply.

Multiply $4$ by $- 2$ .

$5 x - 6 y = - 25$

$- 8 x - 2 (- 3 y) = (- 2) (- 20)$

Multiply $- 3$ by $- 2$ .

$5 x - 6 y = - 25$

$- 8 x + 6 y = (- 2) (- 20)$

$5 x - 6 y = - 25$

$- 8 x + 6 y = (- 2) (- 20)$

$5 x - 6 y = - 25$

$- 8 x + 6 y = (- 2) (- 20)$

$5 x - 6 y = - 25$

$- 8 x + 6 y = (- 2) (- 20)$

Simplify the right side.

Multiply $- 2$ by $- 20$ .

$5 x - 6 y = - 25$

$- 8 x + 6 y = 40$

$5 x - 6 y = - 25$

$- 8 x + 6 y = 40$

$5 x - 6 y = - 25$

$- 8 x + 6 y = 40$

Step 4

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

		$5$	$x$	$-$	$6$	$y$	$=$	$-$	$2$	$5$
$+$	$-$	$8$	$x$	$+$	$6$	$y$	$=$		$4$	$0$
	$-$	$3$	$x$				$=$		$1$	$5$

Step 5

Divide each term in $- 3 x = 15$ by $- 3$ and simplify.

Divide each term in $- 3 x = 15$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{15}{- 3}$

Divide $x$ by $1$ .

$x = \frac{15}{- 3}$

Simplify the right side.

Divide $15$ by $- 3$ .

$x = - 5$

Step 6

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 $y$ .

$5 (- 5) - 6 y = - 25$

Multiply $5$ by $- 5$ .

$- 25 - 6 y = - 25$

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

Add $25$ to both sides of the equation.

$- 6 y = - 25 + 25$

Add $- 25$ and $25$ .

$- 6 y = 0$

Divide each term in $- 6 y = 0$ by $- 6$ and simplify.

Divide each term in $- 6 y = 0$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{0}{- 6}$

Divide $y$ by $1$ .

$y = \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$y = 0$

Step 7

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

$(- 5, 0)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 5, 0)$

Equation Form:

$x = - 5, y = 0$

Step 9

Solve by Addition/Elimination 5x-6y=-25 , 4x-3y+20=0

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