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

$y = - x$ $y = \frac{2}{5} x - 7$

Eliminate the equal sides of each equation and combine.

$- x = \frac{2}{5} x - 7$

Solve $- x = \frac{2}{5} x - 7$ for $x$ .

Combine $\frac{2}{5}$ and $x$ .

$- x = \frac{2 x}{5} - 7$

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

Subtract $\frac{2 x}{5}$ from both sides of the equation.

$- x - \frac{2 x}{5} = - 7$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- x \cdot \frac{5}{5} - \frac{2 x}{5} = - 7$

Combine $- x$ and $\frac{5}{5}$ .

$\frac{- x \cdot 5}{5} - \frac{2 x}{5} = - 7$

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 - 2 x}{5} = - 7$

Simplify the numerator.

Factor $x$ out of $- x \cdot 5 - 2 x$ .

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (- 1 \cdot 5) - 2 x}{5} = - 7$

Factor $x$ out of $- 2 x$ .

$\frac{x (- 1 \cdot 5) + x \cdot - 2}{5} = - 7$

Factor $x$ out of $x (- 1 \cdot 5) + x \cdot - 2$ .

$\frac{x (- 1 \cdot 5 - 2)}{5} = - 7$

Multiply $- 1$ by $5$ .

$\frac{x (- 5 - 2)}{5} = - 7$

Subtract $2$ from $- 5$ .

$\frac{x \cdot - 7}{5} = - 7$

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{5} = - 7$

Move the negative in front of the fraction.

$- \frac{7 x}{5} = - 7$

Multiply both sides of the equation by $- \frac{5}{7}$ .

$- \frac{5}{7} (- \frac{7 x}{5}) = - \frac{5}{7} \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{7} (- \frac{7 x}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{7}$ into the numerator.

$\frac{- 5}{7} (- \frac{7 x}{5}) = - \frac{5}{7} \cdot - 7$

Move the leading negative in $- \frac{7 x}{5}$ into the numerator.

$\frac{- 5}{7} \cdot \frac{- 7 x}{5} = - \frac{5}{7} \cdot - 7$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{7} \cdot \frac{- 7 x}{5} = - \frac{5}{7} \cdot - 7$

Cancel the common factor.

$\frac{5 \cdot - 1}{7} \cdot \frac{- 7 x}{5} = - \frac{5}{7} \cdot - 7$

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{5}{7} \cdot - 7$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{5}{7} \cdot - 7$

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{5}{7} \cdot - 7$

Rewrite the expression.

$- - x = - \frac{5}{7} \cdot - 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{7} \cdot - 7$

Multiply $x$ by $1$ .

$x = - \frac{5}{7} \cdot - 7$

Simplify the right side.

Simplify $- \frac{5}{7} \cdot - 7$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{5}{7}$ into the numerator.

$x = \frac{- 5}{7} \cdot - 7$

Factor $7$ out of $- 7$ .

$x = \frac{- 5}{7} \cdot (7 (- 1))$

Cancel the common factor.

$x = \frac{- 5}{7} \cdot (7 \cdot - 1)$

Rewrite the expression.

$x = - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$x = 5$

Evaluate $y$ when $x = 5$ .

Substitute $5$ for $x$ .

$y = \frac{2}{5} \cdot (5) - 7$

Substitute $5$ for $x$ in $y = \frac{2}{5} \cdot (5) - 7$ and solve for $y$ .

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

$y = \frac{2}{5} \cdot 5 - 7$

Simplify $\frac{2}{5} \cdot 5 - 7$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$y = \frac{2}{5} \cdot 5 - 7$

Rewrite the expression.

$y = 2 - 7$

Subtract $7$ from $2$ .

$y = - 5$

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

$(5, - 5)$

The result can be shown in multiple forms.

Point Form:

$(5, - 5)$

Equation Form:

$x = 5, y = - 5$

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

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