Solve the System of Equations y=x+7 and y=-x+2

$y = x + 7$ and $y = - x + 2$

Eliminate the equal sides of each equation and combine.

$x + 7 = - x + 2$

Solve $x + 7 = - x + 2$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$x + 7 + x = 2$

Add $x$ and $x$ .

$2 x + 7 = 2$

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

Subtract $7$ from both sides of the equation.

$2 x = 2 - 7$

Subtract $7$ from $2$ .

$2 x = - 5$

Divide each term in $2 x = - 5$ by $2$ and simplify.

Divide each term in $2 x = - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Divide $x$ by $1$ .

$x = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

Evaluate $y$ when $x = - \frac{5}{2}$ .

Substitute $- \frac{5}{2}$ for $x$ .

$y = - (- \frac{5}{2}) + 2$

Substitute $- \frac{5}{2}$ for $x$ in $y = - (- \frac{5}{2}) + 2$ and solve for $y$ .

Multiply $- 1$ by $- \frac{5}{2}$ .

$y = \frac{5}{2} + 2$

Simplify $\frac{5}{2} + 2$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{5}{2} + 2 \cdot \frac{2}{2}$

Combine $2$ and $\frac{2}{2}$ .

$y = \frac{5}{2} + \frac{2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{5 + 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$y = \frac{5 + 4}{2}$

Add $5$ and $4$ .

$y = \frac{9}{2}$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- \frac{5}{2}, \frac{9}{2})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{5}{2}, \frac{9}{2})$

Equation Form:

$x = - \frac{5}{2}, y = \frac{9}{2}$

Solve the System of Equations y=x+7 and y=-x+2

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