Solve by Addition/Elimination -2x+7y=10 x-3y=-3

$- 2 x + 7 y = 10$ $x - 3 y = - 3$

Step 1

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

$- 2 x + 7 y = 10$

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

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 x + 7 y = 10$

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

Multiply $- 3$ by $2$ .

$- 2 x + 7 y = 10$

$2 x - 6 y = (2) (- 3)$

$- 2 x + 7 y = 10$

$2 x - 6 y = (2) (- 3)$

$- 2 x + 7 y = 10$

$2 x - 6 y = (2) (- 3)$

Simplify the right side.

Multiply $2$ by $- 3$ .

$- 2 x + 7 y = 10$

$2 x - 6 y = - 6$

$- 2 x + 7 y = 10$

$2 x - 6 y = - 6$

$- 2 x + 7 y = 10$

$2 x - 6 y = - 6$

Step 3

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

	$-$	$2$	$x$	$+$	$7$	$y$	$=$	$1$	$0$
$+$		$2$	$x$	$-$	$6$	$y$	$=$	$-$	$6$
						$y$	$=$		$4$

Step 4

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 $x$ .

$- 2 x + 7 (4) = 10$

Multiply $7$ by $4$ .

$- 2 x + 28 = 10$

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

Subtract $28$ from both sides of the equation.

$- 2 x = 10 - 28$

Subtract $28$ from $10$ .

$- 2 x = - 18$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 18$ by $- 2$ .

$x = 9$

Step 5

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

$(9, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 4)$

Equation Form:

$x = 9, y = 4$

Step 7

Solve by Addition/Elimination -2x+7y=10 x-3y=-3

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