Solve the System of Equations y=-x+2 y=3/5x-6

$y = - x + 2$ $y = \frac{3}{5} x - 6$

Step 1

Eliminate the equal sides of each equation and combine.

$- x + 2 = \frac{3}{5} x - 6$

Step 2

Solve $- x + 2 = \frac{3}{5} x - 6$ for $x$ .

Combine $\frac{3}{5}$ and $x$ .

$- x + 2 = \frac{3 x}{5} - 6$

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

Subtract $\frac{3 x}{5}$ from both sides of the equation.

$- x + 2 - \frac{3 x}{5} = - 6$

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

$- x \cdot \frac{5}{5} - \frac{3 x}{5} + 2 = - 6$

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

$\frac{- x \cdot 5}{5} - \frac{3 x}{5} + 2 = - 6$

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 - 3 x}{5} + 2 = - 6$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x \cdot 5 - 3 x$ .

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

$\frac{x (- 1 \cdot 5) - 3 x}{5} + 2 = - 6$

Factor $x$ out of $- 3 x$ .

$\frac{x (- 1 \cdot 5) + x \cdot - 3}{5} + 2 = - 6$

Factor $x$ out of $x (- 1 \cdot 5) + x \cdot - 3$ .

$\frac{x (- 1 \cdot 5 - 3)}{5} + 2 = - 6$

Multiply $- 1$ by $5$ .

$\frac{x (- 5 - 3)}{5} + 2 = - 6$

Subtract $3$ from $- 5$ .

$\frac{x \cdot - 8}{5} + 2 = - 6$

Move $- 8$ to the left of $x$ .

$\frac{- 8 \cdot x}{5} + 2 = - 6$

Move the negative in front of the fraction.

$- \frac{8 x}{5} + 2 = - 6$

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

Subtract $2$ from both sides of the equation.

$- \frac{8 x}{5} = - 6 - 2$

Subtract $2$ from $- 6$ .

$- \frac{8 x}{5} = - 8$

Multiply both sides of the equation by $- \frac{5}{8}$ .

$- \frac{5}{8} (- \frac{8 x}{5}) = - \frac{5}{8} \cdot - 8$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{8} (- \frac{8 x}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$\frac{- 5}{8} (- \frac{8 x}{5}) = - \frac{5}{8} \cdot - 8$

Move the leading negative in $- \frac{8 x}{5}$ into the numerator.

$\frac{- 5}{8} \cdot \frac{- 8 x}{5} = - \frac{5}{8} \cdot - 8$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{8} \cdot \frac{- 8 x}{5} = - \frac{5}{8} \cdot - 8$

Cancel the common factor.

$\frac{5 \cdot - 1}{8} \cdot \frac{- 8 x}{5} = - \frac{5}{8} \cdot - 8$

Rewrite the expression.

$\frac{- 1}{8} (- 8 x) = - \frac{5}{8} \cdot - 8$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8 x$ .

$\frac{- 1}{8} (8 (- x)) = - \frac{5}{8} \cdot - 8$

Cancel the common factor.

$\frac{- 1}{8} (8 (- x)) = - \frac{5}{8} \cdot - 8$

Rewrite the expression.

$- - x = - \frac{5}{8} \cdot - 8$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{8} \cdot - 8$

Multiply $x$ by $1$ .

$x = - \frac{5}{8} \cdot - 8$

Simplify the right side.

Simplify $- \frac{5}{8} \cdot - 8$ .

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$x = \frac{- 5}{8} \cdot - 8$

Factor $8$ out of $- 8$ .

$x = \frac{- 5}{8} \cdot (8 (- 1))$

Cancel the common factor.

$x = \frac{- 5}{8} \cdot (8 \cdot - 1)$

Rewrite the expression.

$x = - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$x = 5$

Step 3

Evaluate $y$ when $x = 5$ .

Substitute $5$ for $x$ .

$y = \frac{3}{5} \cdot (5) - 6$

Substitute $5$ for $x$ in $y = \frac{3}{5} \cdot (5) - 6$ and solve for $y$ .

Multiply $\frac{3}{5}$ by $5$ .

$y = \frac{3}{5} \cdot 5 - 6$

Simplify $\frac{3}{5} \cdot 5 - 6$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$y = \frac{3}{5} \cdot 5 - 6$

Rewrite the expression.

$y = 3 - 6$

Subtract $6$ from $3$ .

$y = - 3$

Step 4

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

$(5, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, - 3)$

Equation Form:

$x = 5, y = - 3$

Step 6

Solve the System of Equations y=-x+2 y=3/5x-6

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