Solve by Addition/Elimination 5x-2y=3 , -20x+8y=-12

$5 x - 2 y = 3$ , $- 20 x + 8 y = - 12$

Step 1

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

$(4) \cdot (5 x - 2 y) = (4) (3)$

$- 20 x + 8 y = - 12$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$4 (5 x) + 4 (- 2 y) = (4) (3)$

$- 20 x + 8 y = - 12$

Multiply.

Multiply $5$ by $4$ .

$20 x + 4 (- 2 y) = (4) (3)$

$- 20 x + 8 y = - 12$

Multiply $- 2$ by $4$ .

$20 x - 8 y = (4) (3)$

$- 20 x + 8 y = - 12$

$20 x - 8 y = (4) (3)$

$- 20 x + 8 y = - 12$

$20 x - 8 y = (4) (3)$

$- 20 x + 8 y = - 12$

$20 x - 8 y = (4) (3)$

$- 20 x + 8 y = - 12$

Simplify the right side.

Multiply $4$ by $3$ .

$20 x - 8 y = 12$

$- 20 x + 8 y = - 12$

$20 x - 8 y = 12$

$- 20 x + 8 y = - 12$

$20 x - 8 y = 12$

$- 20 x + 8 y = - 12$

Step 3

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

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

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 $20 x$ from both sides of the equation.

$- 8 y = 12 - 20 x$

Divide each term in $- 8 y = 12 - 20 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 12 - 20 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{12}{- 8} + \frac{- 20 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{12}{- 8} + \frac{- 20 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{12}{- 8} + \frac{- 20 x}{- 8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $12$ and $- 8$ .

Factor $4$ out of $12$ .

$y = \frac{4 (3)}{- 8} + \frac{- 20 x}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$y = \frac{4 \cdot 3}{4 \cdot - 2} + \frac{- 20 x}{- 8}$

Cancel the common factor.

$y = \frac{4 \cdot 3}{4 \cdot - 2} + \frac{- 20 x}{- 8}$

Rewrite the expression.

$y = \frac{3}{- 2} + \frac{- 20 x}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{- 20 x}{- 8}$

Cancel the common factor of $- 20$ and $- 8$ .

Factor $- 4$ out of $- 20 x$ .

$y = - \frac{3}{2} + \frac{- 4 (5 x)}{- 8}$

Cancel the common factors.

Factor $- 4$ out of $- 8$ .

$y = - \frac{3}{2} + \frac{- 4 (5 x)}{- 4 (2)}$

Cancel the common factor.

$y = - \frac{3}{2} + \frac{- 4 (5 x)}{- 4 \cdot 2}$

Rewrite the expression.

$y = - \frac{3}{2} + \frac{5 x}{2}$

Step 6

The solution is the set of ordered pairs that make $y = - \frac{3}{2} + \frac{5 x}{2}$ true.

$(x, - \frac{3}{2} + \frac{5 x}{2})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, - \frac{3}{2} + \frac{5 x}{2})$

Equation Form:

$x = x, y = - \frac{3}{2} + \frac{5 x}{2}$

Step 8

Solve by Addition/Elimination 5x-2y=3 , -20x+8y=-12

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