Solve by Addition/Elimination x+7y=12 3x-5y=10

$x + 7 y = 12$ $3 x - 5 y = 10$

Step 1

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

$(- 3) \cdot (x + 7 y) = (- 3) (12)$

$3 x - 5 y = 10$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (x + 7 y)$ .

Apply the distributive property.

$- 3 x - 3 (7 y) = (- 3) (12)$

$3 x - 5 y = 10$

Multiply $7$ by $- 3$ .

$- 3 x - 21 y = (- 3) (12)$

$3 x - 5 y = 10$

$- 3 x - 21 y = (- 3) (12)$

$3 x - 5 y = 10$

$- 3 x - 21 y = (- 3) (12)$

$3 x - 5 y = 10$

Simplify the right side.

Multiply $- 3$ by $12$ .

$- 3 x - 21 y = - 36$

$3 x - 5 y = 10$

$- 3 x - 21 y = - 36$

$3 x - 5 y = 10$

$- 3 x - 21 y = - 36$

$3 x - 5 y = 10$

Step 3

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

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

Step 4

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

Divide each term in $- 26 y = - 26$ by $- 26$ .

$\frac{- 26 y}{- 26} = \frac{- 26}{- 26}$

Simplify the left side.

Cancel the common factor of $- 26$ .

Cancel the common factor.

$\frac{- 26 y}{- 26} = \frac{- 26}{- 26}$

Divide $y$ by $1$ .

$y = \frac{- 26}{- 26}$

Simplify the right side.

Divide $- 26$ by $- 26$ .

$y = 1$

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 $x$ .

$- 3 x - 21 \cdot 1 = - 36$

Multiply $- 21$ by $1$ .

$- 3 x - 21 = - 36$

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

Add $21$ to both sides of the equation.

$- 3 x = - 36 + 21$

Add $- 36$ and $21$ .

$- 3 x = - 15$

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

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

$(5, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, 1)$

Equation Form:

$x = 5, y = 1$

Step 8

Solve by Addition/Elimination x+7y=12 3x-5y=10

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