Solve by Addition/Elimination 2y+7x=-5 5y-7x=12

$2 y + 7 x = - 5$ $5 y - 7 x = 12$

Step 1

Simplify the left side.

Reorder $2 y$ and $7 x$ .

$7 x + 2 y = - 5$

$5 y - 7 x = 12$

$7 x + 2 y = - 5$

$5 y - 7 x = 12$

Step 2

Simplify the left side.

Reorder $5 y$ and $- 7 x$ .

$- 7 x + 5 y = 12$

$7 x + 2 y = - 5$

$- 7 x + 5 y = 12$

$7 x + 2 y = - 5$

Step 3

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

		$7$	$x$	$+$	$2$	$y$	$=$	$-$	$5$
$+$	$-$	$7$	$x$	$+$	$5$	$y$	$=$	$1$	$2$
					$7$	$y$	$=$		$7$

Step 4

Divide each term in $7 y = 7$ by $7$ and simplify.

Divide each term in $7 y = 7$ by $7$ .

$\frac{7 y}{7} = \frac{7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{7}{7}$

Divide $y$ by $1$ .

$y = \frac{7}{7}$

Simplify the right side.

Divide $7$ by $7$ .

$y = 1$

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 $x$ .

$7 x + 2 (1) = - 5$

Multiply $2$ by $1$ .

$7 x + 2 = - 5$

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

Subtract $2$ from both sides of the equation.

$7 x = - 5 - 2$

Subtract $2$ from $- 5$ .

$7 x = - 7$

Divide each term in $7 x = - 7$ by $7$ and simplify.

Divide each term in $7 x = - 7$ by $7$ .

$\frac{7 x}{7} = \frac{- 7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 7}{7}$

Divide $x$ by $1$ .

$x = \frac{- 7}{7}$

Simplify the right side.

Divide $- 7$ by $7$ .

$x = - 1$

Step 6

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

$(- 1, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, 1)$

Equation Form:

$x = - 1, y = 1$

Step 8

Solve by Addition/Elimination 2y+7x=-5 5y-7x=12

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