Solve by Addition/Elimination 5x+y=19 2y=-5x+28

$5 x + y = 19$ $2 y = - 5 x + 28$

Move all terms containing variables to the left side of the equation.

Add $5 x$ to both sides of the equation.

$2 y + 5 x = 28$

$5 x + y = 19$

Reorder $2 y$ and $5 x$ .

$5 x + 2 y = 28$

$5 x + y = 19$

$5 x + 2 y = 28$

$5 x + y = 19$

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

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

$5 x + 2 y = 28$

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$5 x + 2 y = 28$

Multiply $5$ by $- 2$ .

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

$5 x + 2 y = 28$

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

$5 x + 2 y = 28$

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

$5 x + 2 y = 28$

Simplify the right side.

Multiply $- 2$ by $19$ .

$- 10 x - 2 y = - 38$

$5 x + 2 y = 28$

$- 10 x - 2 y = - 38$

$5 x + 2 y = 28$

$- 10 x - 2 y = - 38$

$5 x + 2 y = 28$

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

	$-$	$1$	$0$	$x$	$-$	$2$	$y$	$=$	$-$	$3$	$8$
$+$			$5$	$x$	$+$	$2$	$y$	$=$		$2$	$8$
		$-$	$5$	$x$				$=$	$-$	$1$	$0$

Divide each term in $- 5 x = - 10$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 5}$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$x = 2$

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 $y$ .

$- 10 \cdot 2 - 2 y = - 38$

Multiply $- 10$ by $2$ .

$- 20 - 2 y = - 38$

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

Add $20$ to both sides of the equation.

$- 2 y = - 38 + 20$

Add $- 38$ and $20$ .

$- 2 y = - 18$

Divide each term in $- 2 y = - 18$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 18$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 18}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 18}{- 2}$

Simplify the right side.

Divide $- 18$ by $- 2$ .

$y = 9$

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

$(2, 9)$

The result can be shown in multiple forms.

Point Form:

$(2, 9)$

Equation Form:

$x = 2, y = 9$

Solve by Addition/Elimination 5x+y=19 2y=-5x+28

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