Solve by Addition/Elimination 4x+2y=12 -4x-3y=-16

$4 x + 2 y = 12$ $- 4 x - 3 y = - 16$

Step 1

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

		$4$	$x$	$+$	$2$	$y$	$=$		$1$	$2$
$+$	$-$	$4$	$x$	$-$	$3$	$y$	$=$	$-$	$1$	$6$
					$-$	$y$	$=$		$-$	$4$

Step 2

Divide each term in $- y = - 4$ by $- 1$ and simplify.

Divide each term in $- y = - 4$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 4}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$y = 4$

Step 3

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 $x$ .

$4 x + 2 (4) = 12$

Multiply $2$ by $4$ .

$4 x + 8 = 12$

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

Subtract $8$ from both sides of the equation.

$4 x = 12 - 8$

Subtract $8$ from $12$ .

$4 x = 4$

Divide each term in $4 x = 4$ by $4$ and simplify.

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

Divide $x$ by $1$ .

$x = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

Step 4

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

$(1, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 4)$

Equation Form:

$x = 1, y = 4$

Step 6

Solve by Addition/Elimination 4x+2y=12 -4x-3y=-16

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