Solve by Addition/Elimination 4x-3y=2 , -8x+6y=-4

$4 x - 3 y = 2$ , $- 8 x + 6 y = - 4$

Step 1

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

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

$- 8 x + 6 y = - 4$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$- 8 x + 6 y = - 4$

Multiply.

Multiply $4$ by $2$ .

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

$- 8 x + 6 y = - 4$

Multiply $- 3$ by $2$ .

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

$- 8 x + 6 y = - 4$

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

$- 8 x + 6 y = - 4$

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

$- 8 x + 6 y = - 4$

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

$- 8 x + 6 y = - 4$

Simplify the right side.

Multiply $2$ by $2$ .

$8 x - 6 y = 4$

$- 8 x + 6 y = - 4$

$8 x - 6 y = 4$

$- 8 x + 6 y = - 4$

$8 x - 6 y = 4$

$- 8 x + 6 y = - 4$

Step 3

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

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

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 $8 x$ from both sides of the equation.

$- 6 y = 4 - 8 x$

Divide each term in $- 6 y = 4 - 8 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 4 - 8 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{4}{- 6} + \frac{- 8 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{4}{- 6} + \frac{- 8 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{4}{- 6} + \frac{- 8 x}{- 6}$

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $4$ .

$y = \frac{2 (2)}{- 6} + \frac{- 8 x}{- 6}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$y = \frac{2 \cdot 2}{2 \cdot - 3} + \frac{- 8 x}{- 6}$

Cancel the common factor.

$y = \frac{2 \cdot 2}{2 \cdot - 3} + \frac{- 8 x}{- 6}$

Rewrite the expression.

$y = \frac{2}{- 3} + \frac{- 8 x}{- 6}$

Move the negative in front of the fraction.

$y = - \frac{2}{3} + \frac{- 8 x}{- 6}$

Cancel the common factor of $- 8$ and $- 6$ .

Factor $- 2$ out of $- 8 x$ .

$y = - \frac{2}{3} + \frac{- 2 (4 x)}{- 6}$

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

The solution is the set of ordered pairs that make $y = - \frac{2}{3} + \frac{4 x}{3}$ true.

$(x, - \frac{2}{3} + \frac{4 x}{3})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, - \frac{2}{3} + \frac{4 x}{3})$

Equation Form:

$x = x, y = - \frac{2}{3} + \frac{4 x}{3}$

Step 8

Solve by Addition/Elimination 4x-3y=2 , -8x+6y=-4

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