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

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

Step 1

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

	$3$	$x$	$+$	$2$	$y$	$=$	$1$	$6$
$+$	$2$	$x$	$-$	$2$	$y$	$=$		$4$
	$5$	$x$				$=$	$2$	$0$

Step 2

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

Step 3

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 $y$ .

$3 (4) + 2 y = 16$

Multiply $3$ by $4$ .

$12 + 2 y = 16$

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

Subtract $12$ from both sides of the equation.

$2 y = 16 - 12$

Subtract $12$ from $16$ .

$2 y = 4$

Divide each term in $2 y = 4$ by $2$ and simplify.

Divide each term in $2 y = 4$ by $2$ .

$\frac{2 y}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{4}{2}$

Divide $y$ by $1$ .

$y = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$y = 2$

Step 4

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

$(4, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 6

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

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