Solve by Addition/Elimination 2x-3y=19 , 3x-4y=26

$2 x - 3 y = 19$ , $3 x - 4 y = 26$

Step 1

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

$(- 3) \cdot (2 x - 3 y) = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 3 (2 x) - 3 (- 3 y) = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (- 3 y) = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

Multiply $- 3$ by $- 3$ .

$- 6 x + 9 y = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

$- 6 x + 9 y = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

$- 6 x + 9 y = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

$- 6 x + 9 y = (- 3) (19)$

$(2) \cdot (3 x - 4 y) = (2) (26)$

Simplify the right side.

Multiply $- 3$ by $19$ .

$- 6 x + 9 y = - 57$

$(2) \cdot (3 x - 4 y) = (2) (26)$

$- 6 x + 9 y = - 57$

$(2) \cdot (3 x - 4 y) = (2) (26)$

Simplify the left side.

Simplify $(2) \cdot (3 x - 4 y)$ .

Apply the distributive property.

$- 6 x + 9 y = - 57$

$2 (3 x) + 2 (- 4 y) = (2) (26)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 9 y = - 57$

$6 x + 2 (- 4 y) = (2) (26)$

Multiply $- 4$ by $2$ .

$- 6 x + 9 y = - 57$

$6 x - 8 y = (2) (26)$

$- 6 x + 9 y = - 57$

$6 x - 8 y = (2) (26)$

$- 6 x + 9 y = - 57$

$6 x - 8 y = (2) (26)$

$- 6 x + 9 y = - 57$

$6 x - 8 y = (2) (26)$

Simplify the right side.

Multiply $2$ by $26$ .

$- 6 x + 9 y = - 57$

$6 x - 8 y = 52$

$- 6 x + 9 y = - 57$

$6 x - 8 y = 52$

$- 6 x + 9 y = - 57$

$6 x - 8 y = 52$

Step 3

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

	$-$	$6$	$x$	$+$	$9$	$y$	$=$	$-$	$5$	$7$
$+$		$6$	$x$	$-$	$8$	$y$	$=$		$5$	$2$
						$y$	$=$		$-$	$5$

Step 4

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 $x$ .

$- 6 x + 9 (- 5) = - 57$

Multiply $9$ by $- 5$ .

$- 6 x - 45 = - 57$

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

Add $45$ to both sides of the equation.

$- 6 x = - 57 + 45$

Add $- 57$ and $45$ .

$- 6 x = - 12$

Divide each term in $- 6 x = - 12$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$x = 2$

Step 5

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

$(2, - 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 5)$

Equation Form:

$x = 2, y = - 5$

Step 7

Solve by Addition/Elimination 2x-3y=19 , 3x-4y=26

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