Solve by Addition/Elimination x-3y=-23 5x+6y=74

$x - 3 y = - 23$ $5 x + 6 y = 74$

Step 1

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

$(- 5) \cdot (x - 3 y) = (- 5) (- 23)$

$5 x + 6 y = 74$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 5) \cdot (x - 3 y)$ .

Apply the distributive property.

$- 5 x - 5 (- 3 y) = (- 5) (- 23)$

$5 x + 6 y = 74$

Multiply $- 3$ by $- 5$ .

$- 5 x + 15 y = (- 5) (- 23)$

$5 x + 6 y = 74$

$- 5 x + 15 y = (- 5) (- 23)$

$5 x + 6 y = 74$

$- 5 x + 15 y = (- 5) (- 23)$

$5 x + 6 y = 74$

Simplify the right side.

Multiply $- 5$ by $- 23$ .

$- 5 x + 15 y = 115$

$5 x + 6 y = 74$

$- 5 x + 15 y = 115$

$5 x + 6 y = 74$

$- 5 x + 15 y = 115$

$5 x + 6 y = 74$

Step 3

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

	$-$	$5$	$x$	$+$	$1$	$5$	$y$	$=$	$1$	$1$	$5$
$+$		$5$	$x$	$+$		$6$	$y$	$=$		$7$	$4$
					$2$	$1$	$y$	$=$	$1$	$8$	$9$

Step 4

Divide each term in $21 y = 189$ by $21$ and simplify.

Divide each term in $21 y = 189$ by $21$ .

$\frac{21 y}{21} = \frac{189}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 y}{21} = \frac{189}{21}$

Divide $y$ by $1$ .

$y = \frac{189}{21}$

Simplify the right side.

Divide $189$ by $21$ .

$y = 9$

Step 5

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 $x$ .

$- 5 x + 15 (9) = 115$

Multiply $15$ by $9$ .

$- 5 x + 135 = 115$

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

Subtract $135$ from both sides of the equation.

$- 5 x = 115 - 135$

Subtract $135$ from $115$ .

$- 5 x = - 20$

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 6

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

$(4, 9)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 9)$

Equation Form:

$x = 4, y = 9$

Step 8

Solve by Addition/Elimination x-3y=-23 5x+6y=74

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