Solve by Addition/Elimination 3x+4y=4 6x+4y=16

$3 x + 4 y = 4$ $6 x + 4 y = 16$

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

$(- 1) \cdot (3 x + 4 y) = (- 1) (4)$

$6 x + 4 y = 16$

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (3 x + 4 y)$ .

Apply the distributive property.

$- 1 (3 x) - 1 (4 y) = (- 1) (4)$

$6 x + 4 y = 16$

Multiply.

Multiply $3$ by $- 1$ .

$- 3 x - 1 (4 y) = (- 1) (4)$

$6 x + 4 y = 16$

Multiply $4$ by $- 1$ .

$- 3 x - 4 y = (- 1) (4)$

$6 x + 4 y = 16$

$- 3 x - 4 y = (- 1) (4)$

$6 x + 4 y = 16$

$- 3 x - 4 y = (- 1) (4)$

$6 x + 4 y = 16$

$- 3 x - 4 y = (- 1) (4)$

$6 x + 4 y = 16$

Simplify the right side.

Multiply $- 1$ by $4$ .

$- 3 x - 4 y = - 4$

$6 x + 4 y = 16$

$- 3 x - 4 y = - 4$

$6 x + 4 y = 16$

$- 3 x - 4 y = - 4$

$6 x + 4 y = 16$

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

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

Divide each term in $3 x = 12$ by $3$ and simplify.

Divide each term in $3 x = 12$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3}$

Divide $x$ by $1$ .

$x = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x = 4$

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 $y$ .

$- 3 \cdot 4 - 4 y = - 4$

Multiply $- 3$ by $4$ .

$- 12 - 4 y = - 4$

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

Add $12$ to both sides of the equation.

$- 4 y = - 4 + 12$

Add $- 4$ and $12$ .

$- 4 y = 8$

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

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

$\frac{- 4 y}{- 4} = \frac{8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4}$

Divide $y$ by $1$ .

$y = \frac{8}{- 4}$

Simplify the right side.

Divide $8$ by $- 4$ .

$y = - 2$

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

$(4, - 2)$

The result can be shown in multiple forms.

Point Form:

$(4, - 2)$

Equation Form:

$x = 4, y = - 2$

Solve by Addition/Elimination 3x+4y=4 6x+4y=16

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