Solve by Addition/Elimination -5x+3y=8 , 2x-4y=-20

$- 5 x + 3 y = 8$ , $2 x - 4 y = - 20$

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

$(2) \cdot (- 5 x + 3 y) = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 (- 5 x) + 2 (3 y) = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

Multiply.

Multiply $- 5$ by $2$ .

$- 10 x + 2 (3 y) = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

Multiply $3$ by $2$ .

$- 10 x + 6 y = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

$- 10 x + 6 y = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

$- 10 x + 6 y = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

$- 10 x + 6 y = (2) (8)$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

Simplify the right side.

Multiply $2$ by $8$ .

$- 10 x + 6 y = 16$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

$- 10 x + 6 y = 16$

$(5) \cdot (2 x - 4 y) = (5) (- 20)$

Simplify the left side.

Simplify $(5) \cdot (2 x - 4 y)$ .

Apply the distributive property.

$- 10 x + 6 y = 16$

$5 (2 x) + 5 (- 4 y) = (5) (- 20)$

Multiply.

Multiply $2$ by $5$ .

$- 10 x + 6 y = 16$

$10 x + 5 (- 4 y) = (5) (- 20)$

Multiply $- 4$ by $5$ .

$- 10 x + 6 y = 16$

$10 x - 20 y = (5) (- 20)$

$- 10 x + 6 y = 16$

$10 x - 20 y = (5) (- 20)$

$- 10 x + 6 y = 16$

$10 x - 20 y = (5) (- 20)$

$- 10 x + 6 y = 16$

$10 x - 20 y = (5) (- 20)$

Simplify the right side.

Multiply $5$ by $- 20$ .

$- 10 x + 6 y = 16$

$10 x - 20 y = - 100$

$- 10 x + 6 y = 16$

$10 x - 20 y = - 100$

$- 10 x + 6 y = 16$

$10 x - 20 y = - 100$

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

	$-$	$1$	$0$	$x$	$+$		$6$	$y$	$=$			$1$	$6$
$+$		$1$	$0$	$x$	$-$	$2$	$0$	$y$	$=$	$-$	$1$	$0$	$0$
					$-$	$1$	$4$	$y$	$=$		$-$	$8$	$4$

Divide each term in $- 14 y = - 84$ by $- 14$ and simplify.

Divide each term in $- 14 y = - 84$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{- 84}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{- 84}{- 14}$

Divide $y$ by $1$ .

$y = \frac{- 84}{- 14}$

Simplify the right side.

Divide $- 84$ by $- 14$ .

$y = 6$

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 $x$ .

$- 10 x + 6 (6) = 16$

Multiply $6$ by $6$ .

$- 10 x + 36 = 16$

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

Subtract $36$ from both sides of the equation.

$- 10 x = 16 - 36$

Subtract $36$ from $16$ .

$- 10 x = - 20$

Divide each term in $- 10 x = - 20$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 20$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 20}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 20}{- 10}$

Divide $x$ by $1$ .

$x = \frac{- 20}{- 10}$

Simplify the right side.

Divide $- 20$ by $- 10$ .

$x = 2$

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

$(2, 6)$

The result can be shown in multiple forms.

Point Form:

$(2, 6)$

Equation Form:

$x = 2, y = 6$

Solve by Addition/Elimination -5x+3y=8 , 2x-4y=-20

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