Solve by Addition/Elimination 2x+3y=17 x+5y=19

$2 x + 3 y = 17$ $x + 5 y = 19$

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

$2 x + 3 y = 17$

$(- 2) \cdot (x + 5 y) = (- 2) (19)$

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (x + 5 y)$ .

Apply the distributive property.

$2 x + 3 y = 17$

$- 2 x - 2 (5 y) = (- 2) (19)$

Multiply $5$ by $- 2$ .

$2 x + 3 y = 17$

$- 2 x - 10 y = (- 2) (19)$

$2 x + 3 y = 17$

$- 2 x - 10 y = (- 2) (19)$

$2 x + 3 y = 17$

$- 2 x - 10 y = (- 2) (19)$

Simplify the right side.

Multiply $- 2$ by $19$ .

$2 x + 3 y = 17$

$- 2 x - 10 y = - 38$

$2 x + 3 y = 17$

$- 2 x - 10 y = - 38$

$2 x + 3 y = 17$

$- 2 x - 10 y = - 38$

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

		$2$	$x$	$+$		$3$	$y$	$=$		$1$	$7$
$+$	$-$	$2$	$x$	$-$	$1$	$0$	$y$	$=$	$-$	$3$	$8$
					$-$	$7$	$y$	$=$	$-$	$2$	$1$

Divide each term in $- 7 y = - 21$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 21$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 21}{- 7}$

Divide $y$ by $1$ .

$y = \frac{- 21}{- 7}$

Simplify the right side.

Divide $- 21$ by $- 7$ .

$y = 3$

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 $x$ .

$2 x + 3 (3) = 17$

Multiply $3$ by $3$ .

$2 x + 9 = 17$

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

Subtract $9$ from both sides of the equation.

$2 x = 17 - 9$

Subtract $9$ from $17$ .

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$

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 2x+3y=17 x+5y=19

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