Solve the System of Equations y=-2x+7 and y=5x-7

$y = - 2 x + 7$ and $y = 5 x - 7$

Eliminate the equal sides of each equation and combine.

$- 2 x + 7 = 5 x - 7$

Solve $- 2 x + 7 = 5 x - 7$ for $x$ .

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

Subtract $5 x$ from both sides of the equation.

$- 2 x + 7 - 5 x = - 7$

Subtract $5 x$ from $- 2 x$ .

$- 7 x + 7 = - 7$

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

Subtract $7$ from both sides of the equation.

$- 7 x = - 7 - 7$

Subtract $7$ from $- 7$ .

$- 7 x = - 14$

Divide each term in $- 7 x = - 14$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 14$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 14}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 14}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 7}$

Simplify the right side.

Divide $- 14$ by $- 7$ .

$x = 2$

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

$y = 5 (2) - 7$

Simplify $5 (2) - 7$ .

Multiply $5$ by $2$ .

$y = 10 - 7$

Subtract $7$ from $10$ .

$y = 3$

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

$(2, 3)$

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$