Solve by Addition/Elimination 14x+5y=31 2x-3y=-29

$14 x + 5 y = 31$ $2 x - 3 y = - 29$

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

$14 x + 5 y = 31$

$(- 7) \cdot (2 x - 3 y) = (- 7) (- 29)$

Simplify.

Simplify the left side.

Simplify $(- 7) \cdot (2 x - 3 y)$ .

Apply the distributive property.

$14 x + 5 y = 31$

$- 7 (2 x) - 7 (- 3 y) = (- 7) (- 29)$

Multiply.

Multiply $2$ by $- 7$ .

$14 x + 5 y = 31$

$- 14 x - 7 (- 3 y) = (- 7) (- 29)$

Multiply $- 3$ by $- 7$ .

$14 x + 5 y = 31$

$- 14 x + 21 y = (- 7) (- 29)$

$14 x + 5 y = 31$

$- 14 x + 21 y = (- 7) (- 29)$

$14 x + 5 y = 31$

$- 14 x + 21 y = (- 7) (- 29)$

$14 x + 5 y = 31$

$- 14 x + 21 y = (- 7) (- 29)$

Simplify the right side.

Multiply $- 7$ by $- 29$ .

$14 x + 5 y = 31$

$- 14 x + 21 y = 203$

$14 x + 5 y = 31$

$- 14 x + 21 y = 203$

$14 x + 5 y = 31$

$- 14 x + 21 y = 203$

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

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

Divide each term in $26 y = 234$ by $26$ and simplify.

Divide each term in $26 y = 234$ by $26$ .

$\frac{26 y}{26} = \frac{234}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 y}{26} = \frac{234}{26}$

Divide $y$ by $1$ .

$y = \frac{234}{26}$

Simplify the right side.

Divide $234$ by $26$ .

$y = 9$

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 $x$ .

$14 x + 5 (9) = 31$

Multiply $5$ by $9$ .

$14 x + 45 = 31$

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

Subtract $45$ from both sides of the equation.

$14 x = 31 - 45$

Subtract $45$ from $31$ .

$14 x = - 14$

Divide each term in $14 x = - 14$ by $14$ and simplify.

Divide each term in $14 x = - 14$ by $14$ .

$\frac{14 x}{14} = \frac{- 14}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{- 14}{14}$

Divide $x$ by $1$ .

$x = \frac{- 14}{14}$

Simplify the right side.

Divide $- 14$ by $14$ .

$x = - 1$

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

$(- 1, 9)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 9)$

Equation Form:

$x = - 1, y = 9$

Solve by Addition/Elimination 14x+5y=31 2x-3y=-29

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