Solve by Addition/Elimination 2x-5y=1 3x-4y=-2

$2 x - 5 y = 1$ $3 x - 4 y = - 2$

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

$(- 3) \cdot (2 x - 5 y) = (- 3) (1)$

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

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 3 (2 x) - 3 (- 5 y) = (- 3) (1)$

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

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (- 5 y) = (- 3) (1)$

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

Multiply $- 5$ by $- 3$ .

$- 6 x + 15 y = (- 3) (1)$

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

$- 6 x + 15 y = (- 3) (1)$

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

$- 6 x + 15 y = (- 3) (1)$

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

$- 6 x + 15 y = (- 3) (1)$

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

Simplify the right side.

Multiply $- 3$ by $1$ .

$- 6 x + 15 y = - 3$

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

$- 6 x + 15 y = - 3$

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

Simplify the left side.

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

Apply the distributive property.

$- 6 x + 15 y = - 3$

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

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 15 y = - 3$

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

Multiply $- 4$ by $2$ .

$- 6 x + 15 y = - 3$

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

$- 6 x + 15 y = - 3$

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

$- 6 x + 15 y = - 3$

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

$- 6 x + 15 y = - 3$

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

Simplify the right side.

Multiply $2$ by $- 2$ .

$- 6 x + 15 y = - 3$

$6 x - 8 y = - 4$

$- 6 x + 15 y = - 3$

$6 x - 8 y = - 4$

$- 6 x + 15 y = - 3$

$6 x - 8 y = - 4$

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

	$-$	$6$	$x$	$+$	$1$	$5$	$y$	$=$	$-$	$3$
$+$		$6$	$x$		$-$	$8$	$y$	$=$	$-$	$4$
						$7$	$y$	$=$	$-$	$7$

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 $x$ .

$- 6 x + 15 (- 1) = - 3$

Multiply $15$ by $- 1$ .

$- 6 x - 15 = - 3$

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

Add $15$ to both sides of the equation.

$- 6 x = - 3 + 15$

Add $- 3$ and $15$ .

$- 6 x = 12$

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 $- 6$ .

$x = - 2$

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

$(- 2, - 1)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 1)$

Equation Form:

$x = - 2, y = - 1$

Solve by Addition/Elimination 2x-5y=1 3x-4y=-2

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