Solve by Addition/Elimination -6x+5y=1 , 6x+4y=-10

$- 6 x + 5 y = 1$ , $6 x + 4 y = - 10$

Step 1

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

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

Step 2

Divide each term in $9 y = - 9$ by $9$ and simplify.

Divide each term in $9 y = - 9$ by $9$ .

$\frac{9 y}{9} = \frac{- 9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 9}{9}$

Divide $y$ by $1$ .

$y = \frac{- 9}{9}$

Simplify the right side.

Divide $- 9$ by $9$ .

$y = - 1$

Step 3

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 $x$ .

$- 6 x + 5 (- 1) = 1$

Multiply $5$ by $- 1$ .

$- 6 x - 5 = 1$

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

Add $5$ to both sides of the equation.

$- 6 x = 1 + 5$

Add $1$ and $5$ .

$- 6 x = 6$

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

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

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $- 6$ .

$x = - 1$

Step 4

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

$(- 1, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, - 1)$

Equation Form:

$x = - 1, y = - 1$

Step 6

Solve by Addition/Elimination -6x+5y=1 , 6x+4y=-10

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