Solve by Addition/Elimination 3x-2y=13 , 5x+4y=18

$3 x - 2 y = 13$ , $5 x + 4 y = 18$

Step 1

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

$(2) \cdot (3 x - 2 y) = (2) (13)$

$5 x + 4 y = 18$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 (3 x) + 2 (- 2 y) = (2) (13)$

$5 x + 4 y = 18$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 (- 2 y) = (2) (13)$

$5 x + 4 y = 18$

Multiply $- 2$ by $2$ .

$6 x - 4 y = (2) (13)$

$5 x + 4 y = 18$

$6 x - 4 y = (2) (13)$

$5 x + 4 y = 18$

$6 x - 4 y = (2) (13)$

$5 x + 4 y = 18$

$6 x - 4 y = (2) (13)$

$5 x + 4 y = 18$

Simplify the right side.

Multiply $2$ by $13$ .

$6 x - 4 y = 26$

$5 x + 4 y = 18$

$6 x - 4 y = 26$

$5 x + 4 y = 18$

$6 x - 4 y = 26$

$5 x + 4 y = 18$

Step 3

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

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

Step 4

Divide each term in $11 x = 44$ by $11$ and simplify.

Divide each term in $11 x = 44$ by $11$ .

$\frac{11 x}{11} = \frac{44}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{44}{11}$

Divide $x$ by $1$ .

$x = \frac{44}{11}$

Simplify the right side.

Divide $44$ by $11$ .

$x = 4$

Step 5

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 $y$ .

$6 (4) - 4 y = 26$

Multiply $6$ by $4$ .

$24 - 4 y = 26$

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

Subtract $24$ from both sides of the equation.

$- 4 y = 26 - 24$

Subtract $24$ from $26$ .

$- 4 y = 2$

Divide each term in $- 4 y = 2$ by $- 4$ and simplify.

Divide each term in $- 4 y = 2$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{2}{- 4}$

Divide $y$ by $1$ .

$y = \frac{2}{- 4}$

Simplify the right side.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 1}{2 \cdot - 2}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 2}$

Rewrite the expression.

$y = \frac{1}{- 2}$

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 6

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

$(4, - \frac{1}{2})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, - \frac{1}{2})$

Equation Form:

$x = 4, y = - \frac{1}{2}$

Step 8

Solve by Addition/Elimination 3x-2y=13 , 5x+4y=18

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