Solve by Addition/Elimination 2x-3y=-10 3x+5y=4

$2 x - 3 y = - 10$ $3 x + 5 y = 4$

Step 1

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

$(- 3) \cdot (2 x - 3 y) = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 3 (2 x) - 3 (- 3 y) = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (- 3 y) = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

Multiply $- 3$ by $- 3$ .

$- 6 x + 9 y = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

$- 6 x + 9 y = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

$- 6 x + 9 y = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

$- 6 x + 9 y = (- 3) (- 10)$

$(2) \cdot (3 x + 5 y) = (2) (4)$

Simplify the right side.

Multiply $- 3$ by $- 10$ .

$- 6 x + 9 y = 30$

$(2) \cdot (3 x + 5 y) = (2) (4)$

$- 6 x + 9 y = 30$

$(2) \cdot (3 x + 5 y) = (2) (4)$

Simplify the left side.

Simplify $(2) \cdot (3 x + 5 y)$ .

Apply the distributive property.

$- 6 x + 9 y = 30$

$2 (3 x) + 2 (5 y) = (2) (4)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 9 y = 30$

$6 x + 2 (5 y) = (2) (4)$

Multiply $5$ by $2$ .

$- 6 x + 9 y = 30$

$6 x + 10 y = (2) (4)$

$- 6 x + 9 y = 30$

$6 x + 10 y = (2) (4)$

$- 6 x + 9 y = 30$

$6 x + 10 y = (2) (4)$

$- 6 x + 9 y = 30$

$6 x + 10 y = (2) (4)$

Simplify the right side.

Multiply $2$ by $4$ .

$- 6 x + 9 y = 30$

$6 x + 10 y = 8$

$- 6 x + 9 y = 30$

$6 x + 10 y = 8$

$- 6 x + 9 y = 30$

$6 x + 10 y = 8$

Step 3

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

	$-$	$6$	$x$	$+$		$9$	$y$	$=$	$3$	$0$
$+$		$6$	$x$	$+$	$1$	$0$	$y$	$=$		$8$
					$1$	$9$	$y$	$=$	$3$	$8$

Step 4

Divide each term in $19 y = 38$ by $19$ and simplify.

Divide each term in $19 y = 38$ by $19$ .

$\frac{19 y}{19} = \frac{38}{19}$

Simplify the left side.

Cancel the common factor of $19$ .

Cancel the common factor.

$\frac{19 y}{19} = \frac{38}{19}$

Divide $y$ by $1$ .

$y = \frac{38}{19}$

Simplify the right side.

Divide $38$ by $19$ .

$y = 2$

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 $x$ .

$- 6 x + 9 (2) = 30$

Multiply $9$ by $2$ .

$- 6 x + 18 = 30$

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

Subtract $18$ from both sides of the equation.

$- 6 x = 30 - 18$

Subtract $18$ from $30$ .

$- 6 x = 12$

Divide each term in $- 6 x = 12$ by $- 6$ and simplify.

Divide each term in $- 6 x = 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{12}{- 6}$

Divide $x$ by $1$ .

$x = \frac{12}{- 6}$

Simplify the right side.

Divide $12$ by $- 6$ .

$x = - 2$

Step 6

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

$(- 2, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

Step 8

Solve by Addition/Elimination 2x-3y=-10 3x+5y=4

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