Solve by Addition/Elimination 3x-11y=-1 2x-5y=-3

$3 x - 11 y = - 1$ $2 x - 5 y = - 3$

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

$(- 2) \cdot (3 x - 11 y) = (- 2) (- 1)$

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

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (3 x - 11 y)$ .

Apply the distributive property.

$- 2 (3 x) - 2 (- 11 y) = (- 2) (- 1)$

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

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (- 11 y) = (- 2) (- 1)$

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

Multiply $- 11$ by $- 2$ .

$- 6 x + 22 y = (- 2) (- 1)$

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

$- 6 x + 22 y = (- 2) (- 1)$

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

$- 6 x + 22 y = (- 2) (- 1)$

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

$- 6 x + 22 y = (- 2) (- 1)$

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

Simplify the right side.

Multiply $- 2$ by $- 1$ .

$- 6 x + 22 y = 2$

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

$- 6 x + 22 y = 2$

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

Simplify the left side.

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

Apply the distributive property.

$- 6 x + 22 y = 2$

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

Multiply.

Multiply $2$ by $3$ .

$- 6 x + 22 y = 2$

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

Multiply $- 5$ by $3$ .

$- 6 x + 22 y = 2$

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

$- 6 x + 22 y = 2$

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

$- 6 x + 22 y = 2$

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

$- 6 x + 22 y = 2$

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

Simplify the right side.

Multiply $3$ by $- 3$ .

$- 6 x + 22 y = 2$

$6 x - 15 y = - 9$

$- 6 x + 22 y = 2$

$6 x - 15 y = - 9$

$- 6 x + 22 y = 2$

$6 x - 15 y = - 9$

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

	$-$	$6$	$x$	$+$	$2$	$2$	$y$	$=$		$2$
$+$		$6$	$x$	$-$	$1$	$5$	$y$	$=$	$-$	$9$
						$7$	$y$	$=$	$-$	$7$

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 $7$ .

$y = - 1$

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 $x$ .

$- 6 x + 22 (- 1) = 2$

Multiply $22$ by $- 1$ .

$- 6 x - 22 = 2$

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

Add $22$ to both sides of the equation.

$- 6 x = 2 + 22$

Add $2$ and $22$ .

$- 6 x = 24$

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 $- 6$ .

$x = - 4$

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

$(- 4, - 1)$

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Solve by Addition/Elimination 3x-11y=-1 2x-5y=-3

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