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

$3 x + 2 y = 10$ , $2 x + 5 y = 3$

Step 1

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

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

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

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

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

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (2 y) = (- 2) (10)$

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

Multiply $2$ by $- 2$ .

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

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

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

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

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

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

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

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

Simplify the right side.

Multiply $- 2$ by $10$ .

$- 6 x - 4 y = - 20$

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

$- 6 x - 4 y = - 20$

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

Simplify the left side.

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

Apply the distributive property.

$- 6 x - 4 y = - 20$

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

Multiply.

Multiply $2$ by $3$ .

$- 6 x - 4 y = - 20$

$6 x + 3 (5 y) = (3) (3)$

Multiply $5$ by $3$ .

$- 6 x - 4 y = - 20$

$6 x + 15 y = (3) (3)$

$- 6 x - 4 y = - 20$

$6 x + 15 y = (3) (3)$

$- 6 x - 4 y = - 20$

$6 x + 15 y = (3) (3)$

$- 6 x - 4 y = - 20$

$6 x + 15 y = (3) (3)$

Simplify the right side.

Multiply $3$ by $3$ .

$- 6 x - 4 y = - 20$

$6 x + 15 y = 9$

$- 6 x - 4 y = - 20$

$6 x + 15 y = 9$

$- 6 x - 4 y = - 20$

$6 x + 15 y = 9$

Step 3

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

	$-$	$6$	$x$		$-$	$4$	$y$	$=$	$-$	$2$	$0$
$+$		$6$	$x$	$+$	$1$	$5$	$y$	$=$			$9$
					$1$	$1$	$y$	$=$	$-$	$1$	$1$

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 $x$ .

$- 6 x - 4 \cdot - 1 = - 20$

Multiply $- 4$ by $- 1$ .

$- 6 x + 4 = - 20$

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

Subtract $4$ from both sides of the equation.

$- 6 x = - 20 - 4$

Subtract $4$ from $- 20$ .

$- 6 x = - 24$

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 6

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

$(4, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 8

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

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