Solve by Addition/Elimination 4x-2y=4 6x-4y=6

$4 x - 2 y = 4$ $6 x - 4 y = 6$

Step 1

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

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

$6 x - 4 y = 6$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$6 x - 4 y = 6$

Multiply.

Multiply $4$ by $- 2$ .

$- 8 x - 2 (- 2 y) = (- 2) (4)$

$6 x - 4 y = 6$

Multiply $- 2$ by $- 2$ .

$- 8 x + 4 y = (- 2) (4)$

$6 x - 4 y = 6$

$- 8 x + 4 y = (- 2) (4)$

$6 x - 4 y = 6$

$- 8 x + 4 y = (- 2) (4)$

$6 x - 4 y = 6$

$- 8 x + 4 y = (- 2) (4)$

$6 x - 4 y = 6$

Simplify the right side.

Multiply $- 2$ by $4$ .

$- 8 x + 4 y = - 8$

$6 x - 4 y = 6$

$- 8 x + 4 y = - 8$

$6 x - 4 y = 6$

$- 8 x + 4 y = - 8$

$6 x - 4 y = 6$

Step 3

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

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

Step 4

Divide each term in $- 2 x = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x = 1$

Step 5

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$- 8 \cdot 1 + 4 y = - 8$

Multiply $- 8$ by $1$ .

$- 8 + 4 y = - 8$

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

Add $8$ to both sides of the equation.

$4 y = - 8 + 8$

Add $- 8$ and $8$ .

$4 y = 0$

Divide each term in $4 y = 0$ by $4$ and simplify.

Divide each term in $4 y = 0$ by $4$ .

$\frac{4 y}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{0}{4}$

Divide $y$ by $1$ .

$y = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$y = 0$

Step 6

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

$(1, 0)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, 0)$

Equation Form:

$x = 1, y = 0$

Step 8

Solve by Addition/Elimination 4x-2y=4 6x-4y=6

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