Solve the System of Equations y=-1/3x-3 y=x-7

$y = - \frac{1}{3} x - 3$ $y = x - 7$

Eliminate the equal sides of each equation and combine.

$- \frac{1}{3} x - 3 = x - 7$

Solve $- \frac{1}{3} x - 3 = x - 7$ for $x$ .

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} - 3 = x - 7$

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

Subtract $x$ from both sides of the equation.

$- \frac{x}{3} - 3 - x = - 7$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{3} - x \cdot \frac{3}{3} - 3 = - 7$

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

$- \frac{x}{3} + \frac{- x \cdot 3}{3} - 3 = - 7$

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 3}{3} - 3 = - 7$

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - x \cdot 3}{3} - 3 = - 7$

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

$\frac{x \cdot - 1 + x (- 1 \cdot 3)}{3} - 3 = - 7$

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

$\frac{x (- 1 - 1 \cdot 3)}{3} - 3 = - 7$

Multiply $- 1$ by $3$ .

$\frac{x (- 1 - 3)}{3} - 3 = - 7$

Subtract $3$ from $- 1$ .

$\frac{x \cdot - 4}{3} - 3 = - 7$

Move $- 4$ to the left of $x$ .

$\frac{- 4 \cdot x}{3} - 3 = - 7$

Move the negative in front of the fraction.

$- \frac{4 x}{3} - 3 = - 7$

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

Add $3$ to both sides of the equation.

$- \frac{4 x}{3} = - 7 + 3$

Add $- 7$ and $3$ .

$- \frac{4 x}{3} = - 4$

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 x}{3}) = - \frac{3}{4} \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{4} (- \frac{4 x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 x}{3}) = - \frac{3}{4} \cdot - 4$

Move the leading negative in $- \frac{4 x}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 x}{3} = - \frac{3}{4} \cdot - 4$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 x}{3} = - \frac{3}{4} \cdot - 4$

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 x}{3} = - \frac{3}{4} \cdot - 4$

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) = - \frac{3}{4} \cdot - 4$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) = - \frac{3}{4} \cdot - 4$

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) = - \frac{3}{4} \cdot - 4$

Rewrite the expression.

$- - x = - \frac{3}{4} \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{4} \cdot - 4$

Multiply $x$ by $1$ .

$x = - \frac{3}{4} \cdot - 4$

Simplify the right side.

Simplify $- \frac{3}{4} \cdot - 4$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$x = \frac{- 3}{4} \cdot - 4$

Factor $4$ out of $- 4$ .

$x = \frac{- 3}{4} \cdot (4 (- 1))$

Cancel the common factor.

$x = \frac{- 3}{4} \cdot (4 \cdot - 1)$

Rewrite the expression.

$x = - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$x = 3$

Evaluate $y$ when $x = 3$ .

Substitute $3$ for $x$ .

$y = (3) - 7$

Substitute $3$ for $x$ in $y = (3) - 7$ and solve for $y$ .

Remove parentheses.

$y = 3 - 7$

Remove parentheses.

$y = (3) - 7$

Subtract $7$ from $3$ .

$y = - 4$

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

$(3, - 4)$

The result can be shown in multiple forms.

Point Form:

$(3, - 4)$

Equation Form:

$x = 3, y = - 4$

Solve the System of Equations y=-1/3x-3 y=x-7

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