Solve by Addition/Elimination 4x+3y=6 -4x+2y=14

$4 x + 3 y = 6$ $- 4 x + 2 y = 14$

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $20$ by $5$ .

$y = 4$

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 $x$ .

$4 x + 3 (4) = 6$

Multiply $3$ by $4$ .

$4 x + 12 = 6$

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

Subtract $12$ from both sides of the equation.

$4 x = 6 - 12$

Subtract $12$ from $6$ .

$4 x = - 6$

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

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

$\frac{4 x}{4} = \frac{- 6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 6}{4}$

Divide $x$ by $1$ .

$x = \frac{- 6}{4}$

Simplify the right side.

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

Factor $2$ out of $- 6$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 3}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 3}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 3}{2}$

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

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

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

The result can be shown in multiple forms.

Point Form:

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

Equation Form:

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

Solve by Addition/Elimination 4x+3y=6 -4x+2y=14

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