Solve by Addition/Elimination x+y=7 x-y=-1

$x + y = 7$ $x - y = - 1$

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

$x + y = 7$

$(- 1) \cdot (x - y) = (- 1) (- 1)$

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (x - y)$ .

Apply the distributive property.

$x + y = 7$

$- 1 x - 1 (- y) = (- 1) (- 1)$

Rewrite $- 1 x$ as $- x$ .

$x + y = 7$

$- x - 1 (- y) = (- 1) (- 1)$

Multiply $- 1 (- y)$ .

Multiply $- 1$ by $- 1$ .

$x + y = 7$

$- x + 1 y = (- 1) (- 1)$

Multiply $y$ by $1$ .

$x + y = 7$

$- x + y = (- 1) (- 1)$

$x + y = 7$

$- x + y = (- 1) (- 1)$

$x + y = 7$

$- x + y = (- 1) (- 1)$

$x + y = 7$

$- x + y = (- 1) (- 1)$

Simplify the right side.

Multiply $- 1$ by $- 1$ .

$x + y = 7$

$- x + y = 1$

$x + y = 7$

$- x + y = 1$

$x + y = 7$

$- x + y = 1$

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $8$ by $2$ .

$y = 4$

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 $x$ .

$x + 4 = 7$

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

Subtract $4$ from both sides of the equation.

$x = 7 - 4$

Subtract $4$ from $7$ .

$x = 3$

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

$(3, 4)$

The result can be shown in multiple forms.

Point Form:

$(3, 4)$

Equation Form:

$x = 3, y = 4$

Solve by Addition/Elimination x+y=7 x-y=-1

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