Solve the System of Equations 7x-y=-13 and -3x-y=-3

$7 x - y = - 13$ and $- 3 x - y = - 3$

Solve for $x$ in $7 x - y = - 13$ .

Add $y$ to both sides of the equation.

$7 x = - 13 + y$

$- 3 x - y = - 3$

Divide each term in $7 x = - 13 + y$ by $7$ and simplify.

Divide each term in $7 x = - 13 + y$ by $7$ .

$\frac{7 x}{7} = \frac{- 13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

Divide $x$ by $1$ .

$x = \frac{- 13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

$x = \frac{- 13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

$x = \frac{- 13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 3 x - y = - 3$

Replace all occurrences of $x$ with $- \frac{13}{7} + \frac{y}{7}$ in each equation.

Replace all occurrences of $x$ in $- 3 x - y = - 3$ with $- \frac{13}{7} + \frac{y}{7}$ .

$- 3 (- \frac{13}{7} + \frac{y}{7}) - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Simplify the left side.

Simplify $- 3 (- \frac{13}{7} + \frac{y}{7}) - y$ .

Simplify each term.

Apply the distributive property.

$- 3 (- \frac{13}{7}) - 3 \frac{y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Multiply $- 3 (- \frac{13}{7})$ .

Multiply $- 1$ by $- 3$ .

$3 (\frac{13}{7}) - 3 \frac{y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Combine $3$ and $\frac{13}{7}$ .

$\frac{3 \cdot 13}{7} - 3 \frac{y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Multiply $3$ by $13$ .

$\frac{39}{7} - 3 \frac{y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$\frac{39}{7} - 3 \frac{y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Combine $- 3$ and $\frac{y}{7}$ .

$\frac{39}{7} + \frac{- 3 y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Move the negative in front of the fraction.

$\frac{39}{7} - \frac{3 y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$\frac{39}{7} - \frac{3 y}{7} - y = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

To write $- y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{39}{7} - \frac{3 y}{7} - y \cdot \frac{7}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Combine $- y$ and $\frac{7}{7}$ .

$\frac{39}{7} - \frac{3 y}{7} + \frac{- y \cdot 7}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Combine the numerators over the common denominator.

$\frac{39}{7} + \frac{- 3 y - y \cdot 7}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Combine the numerators over the common denominator.

$\frac{39 - 3 y - y \cdot 7}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Multiply $7$ by $- 1$ .

$\frac{39 - 3 y - 7 y}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Subtract $7 y$ from $- 3 y$ .

$\frac{39 - 10 y}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$\frac{39 - 10 y}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$\frac{39 - 10 y}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

$\frac{39 - 10 y}{7} = - 3$

$x = - \frac{13}{7} + \frac{y}{7}$

Solve for $y$ in $\frac{39 - 10 y}{7} = - 3$ .

Multiply both sides by $7$ .

$\frac{39 - 10 y}{7} \cdot 7 = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

Simplify.

Simplify the left side.

Simplify $\frac{39 - 10 y}{7} \cdot 7$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{39 - 10 y}{7} \cdot 7 = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

Rewrite the expression.

$39 - 10 y = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

$39 - 10 y = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

Reorder $39$ and $- 10 y$ .

$- 10 y + 39 = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 10 y + 39 = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 10 y + 39 = - 3 \cdot 7$

$x = - \frac{13}{7} + \frac{y}{7}$

Simplify the right side.

Multiply $- 3$ by $7$ .

$- 10 y + 39 = - 21$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 10 y + 39 = - 21$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 10 y + 39 = - 21$

$x = - \frac{13}{7} + \frac{y}{7}$

Solve for $y$ .

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

Subtract $39$ from both sides of the equation.

$- 10 y = - 21 - 39$

$x = - \frac{13}{7} + \frac{y}{7}$

Subtract $39$ from $- 21$ .

$- 10 y = - 60$

$x = - \frac{13}{7} + \frac{y}{7}$

$- 10 y = - 60$

$x = - \frac{13}{7} + \frac{y}{7}$

Divide each term in $- 10 y = - 60$ by $- 10$ and simplify.

Divide each term in $- 10 y = - 60$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 60}{- 10}$

$x = - \frac{13}{7} + \frac{y}{7}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 60}{- 10}$

$x = - \frac{13}{7} + \frac{y}{7}$

Divide $y$ by $1$ .

$y = \frac{- 60}{- 10}$

$x = - \frac{13}{7} + \frac{y}{7}$

$y = \frac{- 60}{- 10}$

$x = - \frac{13}{7} + \frac{y}{7}$

$y = \frac{- 60}{- 10}$

$x = - \frac{13}{7} + \frac{y}{7}$

Simplify the right side.

Divide $- 60$ by $- 10$ .

$y = 6$

$x = - \frac{13}{7} + \frac{y}{7}$

$y = 6$

$x = - \frac{13}{7} + \frac{y}{7}$

$y = 6$

$x = - \frac{13}{7} + \frac{y}{7}$

$y = 6$

$x = - \frac{13}{7} + \frac{y}{7}$

$y = 6$

$x = - \frac{13}{7} + \frac{y}{7}$

Replace all occurrences of $y$ with $6$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{13}{7} + \frac{y}{7}$ with $6$ .

$x = - \frac{13}{7} + \frac{6}{7}$

$y = 6$

Simplify the right side.

Simplify $- \frac{13}{7} + \frac{6}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 13 + 6}{7}$

$y = 6$

Simplify the expression.

Add $- 13$ and $6$ .

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

$y = 6$

Divide $- 7$ by $7$ .

$x = - 1$

$y = 6$

$x = - 1$

$y = 6$

$x = - 1$

$y = 6$

$x = - 1$

$y = 6$

$x = - 1$

$y = 6$

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

$(- 1, 6)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 6)$

Equation Form:

$x = - 1, y = 6$

Solve the System of Equations 7x-y=-13 and -3x-y=-3

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