Solve the System of Equations x+7y=5 and -3x-8y=11

$x + 7 y = 5$ and $- 3 x - 8 y = 11$

Subtract $7 y$ from both sides of the equation.

$x = 5 - 7 y$

$- 3 x - 8 y = 11$

Replace all occurrences of $x$ with $5 - 7 y$ in each equation.

Replace all occurrences of $x$ in $- 3 x - 8 y = 11$ with $5 - 7 y$ .

$- 3 (5 - 7 y) - 8 y = 11$

$x = 5 - 7 y$

Simplify the left side.

Simplify $- 3 (5 - 7 y) - 8 y$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot 5 - 3 (- 7 y) - 8 y = 11$

$x = 5 - 7 y$

Multiply $- 3$ by $5$ .

$- 15 - 3 (- 7 y) - 8 y = 11$

$x = 5 - 7 y$

Multiply $- 7$ by $- 3$ .

$- 15 + 21 y - 8 y = 11$

$x = 5 - 7 y$

$- 15 + 21 y - 8 y = 11$

$x = 5 - 7 y$

Subtract $8 y$ from $21 y$ .

$- 15 + 13 y = 11$

$x = 5 - 7 y$

$- 15 + 13 y = 11$

$x = 5 - 7 y$

$- 15 + 13 y = 11$

$x = 5 - 7 y$

$- 15 + 13 y = 11$

$x = 5 - 7 y$

Solve for $y$ in $- 15 + 13 y = 11$ .

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

Add $15$ to both sides of the equation.

$13 y = 11 + 15$

$x = 5 - 7 y$

Add $11$ and $15$ .

$13 y = 26$

$x = 5 - 7 y$

$13 y = 26$

$x = 5 - 7 y$

Divide each term in $13 y = 26$ by $13$ and simplify.

Divide each term in $13 y = 26$ by $13$ .

$\frac{13 y}{13} = \frac{26}{13}$

$x = 5 - 7 y$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 y}{13} = \frac{26}{13}$

$x = 5 - 7 y$

Divide $y$ by $1$ .

$y = \frac{26}{13}$

$x = 5 - 7 y$

$y = \frac{26}{13}$

$x = 5 - 7 y$

$y = \frac{26}{13}$

$x = 5 - 7 y$

Simplify the right side.

Divide $26$ by $13$ .

$y = 2$

$x = 5 - 7 y$

$y = 2$

$x = 5 - 7 y$

$y = 2$

$x = 5 - 7 y$

$y = 2$

$x = 5 - 7 y$

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = 5 - 7 y$ with $2$ .

$x = 5 - 7 \cdot 2$

$y = 2$

Simplify the right side.

Simplify $5 - 7 \cdot 2$ .

Multiply $- 7$ by $2$ .

$x = 5 - 14$

$y = 2$

Subtract $14$ from $5$ .

$x = - 9$

$y = 2$

$x = - 9$

$y = 2$

$x = - 9$

$y = 2$

$x = - 9$

$y = 2$

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

$(- 9, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 9, 2)$

Equation Form:

$x = - 9, y = 2$

Solve the System of Equations x+7y=5 and -3x-8y=11

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