Solve by Addition/Elimination 2x+3y=18 5x-y=11

$2 x + 3 y = 18$ $5 x - y = 11$

Step 1

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

$2 x + 3 y = 18$

$(3) \cdot (5 x - y) = (3) (11)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 x + 3 y = 18$

$3 (5 x) + 3 (- y) = (3) (11)$

Multiply.

Multiply $5$ by $3$ .

$2 x + 3 y = 18$

$15 x + 3 (- y) = (3) (11)$

Multiply $- 1$ by $3$ .

$2 x + 3 y = 18$

$15 x - 3 y = (3) (11)$

$2 x + 3 y = 18$

$15 x - 3 y = (3) (11)$

$2 x + 3 y = 18$

$15 x - 3 y = (3) (11)$

$2 x + 3 y = 18$

$15 x - 3 y = (3) (11)$

Simplify the right side.

Multiply $3$ by $11$ .

$2 x + 3 y = 18$

$15 x - 3 y = 33$

$2 x + 3 y = 18$

$15 x - 3 y = 33$

$2 x + 3 y = 18$

$15 x - 3 y = 33$

Step 3

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

		$2$	$x$	$+$	$3$	$y$	$=$	$1$	$8$
$+$	$1$	$5$	$x$	$-$	$3$	$y$	$=$	$3$	$3$
	$1$	$7$	$x$				$=$	$5$	$1$

Step 4

Divide each term in $17 x = 51$ by $17$ and simplify.

Divide each term in $17 x = 51$ by $17$ .

$\frac{17 x}{17} = \frac{51}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} = \frac{51}{17}$

Divide $x$ by $1$ .

$x = \frac{51}{17}$

Simplify the right side.

Divide $51$ by $17$ .

$x = 3$

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 $y$ .

$2 (3) + 3 y = 18$

Multiply $2$ by $3$ .

$6 + 3 y = 18$

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

Subtract $6$ from both sides of the equation.

$3 y = 18 - 6$

Subtract $6$ from $18$ .

$3 y = 12$

Divide each term in $3 y = 12$ by $3$ and simplify.

Divide each term in $3 y = 12$ by $3$ .

$\frac{3 y}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{12}{3}$

Divide $y$ by $1$ .

$y = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$y = 4$

Step 6

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

$(3, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, 4)$

Equation Form:

$x = 3, y = 4$

Step 8

Solve by Addition/Elimination 2x+3y=18 5x-y=11

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