Solve by Addition/Elimination 2x-5y=22 2x-3y=6

$2 x - 5 y = 22$ $2 x - 3 y = 6$

Step 1

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

$(- 1) \cdot (2 x - 5 y) = (- 1) (22)$

$2 x - 3 y = 6$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (2 x - 5 y)$ .

Apply the distributive property.

$- 1 (2 x) - 1 (- 5 y) = (- 1) (22)$

$2 x - 3 y = 6$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 x - 1 (- 5 y) = (- 1) (22)$

$2 x - 3 y = 6$

Multiply $- 5$ by $- 1$ .

$- 2 x + 5 y = (- 1) (22)$

$2 x - 3 y = 6$

$- 2 x + 5 y = (- 1) (22)$

$2 x - 3 y = 6$

$- 2 x + 5 y = (- 1) (22)$

$2 x - 3 y = 6$

$- 2 x + 5 y = (- 1) (22)$

$2 x - 3 y = 6$

Simplify the right side.

Multiply $- 1$ by $22$ .

$- 2 x + 5 y = - 22$

$2 x - 3 y = 6$

$- 2 x + 5 y = - 22$

$2 x - 3 y = 6$

$- 2 x + 5 y = - 22$

$2 x - 3 y = 6$

Step 3

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

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

Step 4

Divide each term in $2 y = - 16$ by $2$ and simplify.

Divide each term in $2 y = - 16$ by $2$ .

$\frac{2 y}{2} = \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 16}{2}$

Divide $y$ by $1$ .

$y = \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$y = - 8$

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 $x$ .

$- 2 x + 5 (- 8) = - 22$

Multiply $5$ by $- 8$ .

$- 2 x - 40 = - 22$

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

Add $40$ to both sides of the equation.

$- 2 x = - 22 + 40$

Add $- 22$ and $40$ .

$- 2 x = 18$

Divide each term in $- 2 x = 18$ by $- 2$ and simplify.

Divide each term in $- 2 x = 18$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{18}{- 2}$

Divide $x$ by $1$ .

$x = \frac{18}{- 2}$

Simplify the right side.

Divide $18$ by $- 2$ .

$x = - 9$

Step 6

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

$(- 9, - 8)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 9, - 8)$

Equation Form:

$x = - 9, y = - 8$

Step 8

Solve by Addition/Elimination 2x-5y=22 2x-3y=6

Related Questions

Support LCMGCF.com by disabling your adblocker.