Solve by Addition/Elimination x+3y=5 x=-6y+14

$x + 3 y = 5$ $x = - 6 y + 14$

Add $6 y$ to both sides of the equation.

$x + 6 y = 14$

$x + 3 y = 5$

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

$x + 3 y = 5$

$(- 1) \cdot (x + 6 y) = (- 1) (14)$

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (x + 6 y)$ .

Apply the distributive property.

$x + 3 y = 5$

$- 1 x - 1 (6 y) = (- 1) (14)$

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

$x + 3 y = 5$

$- x - 1 (6 y) = (- 1) (14)$

Multiply $6$ by $- 1$ .

$x + 3 y = 5$

$- x - 6 y = (- 1) (14)$

$x + 3 y = 5$

$- x - 6 y = (- 1) (14)$

$x + 3 y = 5$

$- x - 6 y = (- 1) (14)$

$x + 3 y = 5$

$- x - 6 y = (- 1) (14)$

Simplify the right side.

Multiply $- 1$ by $14$ .

$x + 3 y = 5$

$- x - 6 y = - 14$

$x + 3 y = 5$

$- x - 6 y = - 14$

$x + 3 y = 5$

$- x - 6 y = - 14$

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

		$x$	$+$	$3$	$y$	$=$			$5$
$+$	$-$	$x$	$-$	$6$	$y$	$=$	$-$	$1$	$4$
			$-$	$3$	$y$	$=$		$-$	$9$

Divide each term in $- 3 y = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 9$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 9}{- 3}$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$y = 3$

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 $x$ .

$x + 3 (3) = 5$

Multiply $3$ by $3$ .

$x + 9 = 5$

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

Subtract $9$ from both sides of the equation.

$x = 5 - 9$

Subtract $9$ from $5$ .

$x = - 4$

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

$(- 4, 3)$

The result can be shown in multiple forms.

Point Form:

$(- 4, 3)$

Equation Form:

$x = - 4, y = 3$

Solve by Addition/Elimination x+3y=5 x=-6y+14

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