Solve the System of Equations y=-2x-2 7y-49=-49x

$y = - 2 x - 2$ $7 y - 49 = - 49 x$

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

Replace all occurrences of $y$ in $7 y - 49 = - 49 x$ with $- 2 x - 2$ .

$7 (- 2 x - 2) - 49 = - 49 x$

$y = - 2 x - 2$

Simplify the left side.

Simplify $7 (- 2 x - 2) - 49$ .

Simplify each term.

Apply the distributive property.

$7 (- 2 x) + 7 \cdot - 2 - 49 = - 49 x$

$y = - 2 x - 2$

Multiply $- 2$ by $7$ .

$- 14 x + 7 \cdot - 2 - 49 = - 49 x$

$y = - 2 x - 2$

Multiply $7$ by $- 2$ .

$- 14 x - 14 - 49 = - 49 x$

$y = - 2 x - 2$

$- 14 x - 14 - 49 = - 49 x$

$y = - 2 x - 2$

Subtract $49$ from $- 14$ .

$- 14 x - 63 = - 49 x$

$y = - 2 x - 2$

$- 14 x - 63 = - 49 x$

$y = - 2 x - 2$

$- 14 x - 63 = - 49 x$

$y = - 2 x - 2$

$- 14 x - 63 = - 49 x$

$y = - 2 x - 2$

Solve for $x$ in $- 14 x - 63 = - 49 x$ .

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

Add $49 x$ to both sides of the equation.

$- 14 x - 63 + 49 x = 0$

$y = - 2 x - 2$

Add $- 14 x$ and $49 x$ .

$35 x - 63 = 0$

$y = - 2 x - 2$

$35 x - 63 = 0$

$y = - 2 x - 2$

Add $63$ to both sides of the equation.

$35 x = 63$

$y = - 2 x - 2$

Divide each term in $35 x = 63$ by $35$ and simplify.

Divide each term in $35 x = 63$ by $35$ .

$\frac{35 x}{35} = \frac{63}{35}$

$y = - 2 x - 2$

Simplify the left side.

Cancel the common factor of $35$ .

Cancel the common factor.

$\frac{35 x}{35} = \frac{63}{35}$

$y = - 2 x - 2$

Divide $x$ by $1$ .

$x = \frac{63}{35}$

$y = - 2 x - 2$

$x = \frac{63}{35}$

$y = - 2 x - 2$

$x = \frac{63}{35}$

$y = - 2 x - 2$

Simplify the right side.

Cancel the common factor of $63$ and $35$ .

Factor $7$ out of $63$ .

$x = \frac{7 (9)}{35}$

$y = - 2 x - 2$

Cancel the common factors.

Factor $7$ out of $35$ .

$x = \frac{7 \cdot 9}{7 \cdot 5}$

$y = - 2 x - 2$

Cancel the common factor.

$x = \frac{7 \cdot 9}{7 \cdot 5}$

$y = - 2 x - 2$

Rewrite the expression.

$x = \frac{9}{5}$

$y = - 2 x - 2$

$x = \frac{9}{5}$

$y = - 2 x - 2$

$x = \frac{9}{5}$

$y = - 2 x - 2$

$x = \frac{9}{5}$

$y = - 2 x - 2$

$x = \frac{9}{5}$

$y = - 2 x - 2$

$x = \frac{9}{5}$

$y = - 2 x - 2$

Replace all occurrences of $x$ with $\frac{9}{5}$ in each equation.

Replace all occurrences of $x$ in $y = - 2 x - 2$ with $\frac{9}{5}$ .

$y = - 2 (\frac{9}{5}) - 2$

$x = \frac{9}{5}$

Simplify the right side.

Simplify $- 2 (\frac{9}{5}) - 2$ .

Simplify each term.

Multiply $- 2 (\frac{9}{5})$ .

Combine $- 2$ and $\frac{9}{5}$ .

$y = \frac{- 2 \cdot 9}{5} - 2$

$x = \frac{9}{5}$

Multiply $- 2$ by $9$ .

$y = \frac{- 18}{5} - 2$

$x = \frac{9}{5}$

$y = \frac{- 18}{5} - 2$

$x = \frac{9}{5}$

Move the negative in front of the fraction.

$y = - \frac{18}{5} - 2$

$x = \frac{9}{5}$

$y = - \frac{18}{5} - 2$

$x = \frac{9}{5}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{18}{5} - 2 \cdot \frac{5}{5}$

$x = \frac{9}{5}$

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

$y = - \frac{18}{5} + \frac{- 2 \cdot 5}{5}$

$x = \frac{9}{5}$

Combine the numerators over the common denominator.

$y = \frac{- 18 - 2 \cdot 5}{5}$

$x = \frac{9}{5}$

Simplify the numerator.

Multiply $- 2$ by $5$ .

$y = \frac{- 18 - 10}{5}$

$x = \frac{9}{5}$

Subtract $10$ from $- 18$ .

$y = \frac{- 28}{5}$

$x = \frac{9}{5}$

$y = \frac{- 28}{5}$

$x = \frac{9}{5}$

Move the negative in front of the fraction.

$y = - \frac{28}{5}$

$x = \frac{9}{5}$

$y = - \frac{28}{5}$

$x = \frac{9}{5}$

$y = - \frac{28}{5}$

$x = \frac{9}{5}$

$y = - \frac{28}{5}$

$x = \frac{9}{5}$

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

$(\frac{9}{5}, - \frac{28}{5})$

The result can be shown in multiple forms.

Point Form:

$(\frac{9}{5}, - \frac{28}{5})$

Equation Form:

$x = \frac{9}{5}, y = - \frac{28}{5}$

Solve the System of Equations y=-2x-2 7y-49=-49x

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