Solve by Addition/Elimination 4x-3y=-15 2x+7y=35

$4 x - 3 y = - 15$ $2 x + 7 y = 35$

Step 1

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

$4 x - 3 y = - 15$

$(- 2) \cdot (2 x + 7 y) = (- 2) (35)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (2 x + 7 y)$ .

Apply the distributive property.

$4 x - 3 y = - 15$

$- 2 (2 x) - 2 (7 y) = (- 2) (35)$

Multiply.

Multiply $2$ by $- 2$ .

$4 x - 3 y = - 15$

$- 4 x - 2 (7 y) = (- 2) (35)$

Multiply $7$ by $- 2$ .

$4 x - 3 y = - 15$

$- 4 x - 14 y = (- 2) (35)$

$4 x - 3 y = - 15$

$- 4 x - 14 y = (- 2) (35)$

$4 x - 3 y = - 15$

$- 4 x - 14 y = (- 2) (35)$

$4 x - 3 y = - 15$

$- 4 x - 14 y = (- 2) (35)$

Simplify the right side.

Multiply $- 2$ by $35$ .

$4 x - 3 y = - 15$

$- 4 x - 14 y = - 70$

$4 x - 3 y = - 15$

$- 4 x - 14 y = - 70$

$4 x - 3 y = - 15$

$- 4 x - 14 y = - 70$

Step 3

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

		$4$	$x$		$-$	$3$	$y$	$=$	$-$	$1$	$5$
$+$	$-$	$4$	$x$	$-$	$1$	$4$	$y$	$=$	$-$	$7$	$0$
				$-$	$1$	$7$	$y$	$=$	$-$	$8$	$5$

Step 4

Divide each term in $- 17 y = - 85$ by $- 17$ and simplify.

Divide each term in $- 17 y = - 85$ by $- 17$ .

$\frac{- 17 y}{- 17} = \frac{- 85}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 y}{- 17} = \frac{- 85}{- 17}$

Divide $y$ by $1$ .

$y = \frac{- 85}{- 17}$

Simplify the right side.

Divide $- 85$ by $- 17$ .

$y = 5$

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 $x$ .

$4 x - 3 \cdot 5 = - 15$

Multiply $- 3$ by $5$ .

$4 x - 15 = - 15$

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

Add $15$ to both sides of the equation.

$4 x = - 15 + 15$

Add $- 15$ and $15$ .

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

Step 6

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

$(0, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0, 5)$

Equation Form:

$x = 0, y = 5$

Step 8

Solve by Addition/Elimination 4x-3y=-15 2x+7y=35

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