Solve by Addition/Elimination 4x-6y=-26 -2x+3y=13

$4 x - 6 y = - 26$ $- 2 x + 3 y = 13$

Step 1

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

$4 x - 6 y = - 26$

$(2) \cdot (- 2 x + 3 y) = (2) (13)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$4 x - 6 y = - 26$

$2 (- 2 x) + 2 (3 y) = (2) (13)$

Multiply.

Multiply $- 2$ by $2$ .

$4 x - 6 y = - 26$

$- 4 x + 2 (3 y) = (2) (13)$

Multiply $3$ by $2$ .

$4 x - 6 y = - 26$

$- 4 x + 6 y = (2) (13)$

$4 x - 6 y = - 26$

$- 4 x + 6 y = (2) (13)$

$4 x - 6 y = - 26$

$- 4 x + 6 y = (2) (13)$

$4 x - 6 y = - 26$

$- 4 x + 6 y = (2) (13)$

Simplify the right side.

Multiply $2$ by $13$ .

$4 x - 6 y = - 26$

$- 4 x + 6 y = 26$

$4 x - 6 y = - 26$

$- 4 x + 6 y = 26$

$4 x - 6 y = - 26$

$- 4 x + 6 y = 26$

Step 3

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

		$4$	$x$	$-$	$6$	$y$	$=$	$-$	$2$	$6$
$+$	$-$	$4$	$x$	$+$	$6$	$y$	$=$		$2$	$6$
						$0$	$=$			$0$

Step 4

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 5

Solve one of the equations for $y$ .

Subtract $4 x$ from both sides of the equation.

$- 6 y = - 26 - 4 x$

Divide each term in $- 6 y = - 26 - 4 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 26 - 4 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 26}{- 6} + \frac{- 4 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 26}{- 6} + \frac{- 4 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 26}{- 6} + \frac{- 4 x}{- 6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 26$ and $- 6$ .

Factor $- 2$ out of $- 26$ .

$y = \frac{- 2 (13)}{- 6} + \frac{- 4 x}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = \frac{- 2 \cdot 13}{- 2 \cdot 3} + \frac{- 4 x}{- 6}$

Cancel the common factor.

$y = \frac{- 2 \cdot 13}{- 2 \cdot 3} + \frac{- 4 x}{- 6}$

Rewrite the expression.

$y = \frac{13}{3} + \frac{- 4 x}{- 6}$

Cancel the common factor of $- 4$ and $- 6$ .

Factor $- 2$ out of $- 4 x$ .

$y = \frac{13}{3} + \frac{- 2 (2 x)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = \frac{13}{3} + \frac{- 2 (2 x)}{- 2 (3)}$

Cancel the common factor.

$y = \frac{13}{3} + \frac{- 2 (2 x)}{- 2 \cdot 3}$

Rewrite the expression.

$y = \frac{13}{3} + \frac{2 x}{3}$

Step 6

The solution is the set of ordered pairs that make $y = \frac{13}{3} + \frac{2 x}{3}$ true.

$(x, \frac{13}{3} + \frac{2 x}{3})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, \frac{13}{3} + \frac{2 x}{3})$

Equation Form:

$x = x, y = \frac{13}{3} + \frac{2 x}{3}$

Step 8

Solve by Addition/Elimination 4x-6y=-26 -2x+3y=13

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