Solve the System of Equations -14=-20y-7x 10y+4=2x

$- 14 = - 20 y - 7 x$ $10 y + 4 = 2 x$

Solve for $y$ in $10 y + 4 = 2 x$ .

Subtract $4$ from both sides of the equation.

$10 y = 2 x - 4$

$- 14 = - 20 y - 7 x$

Divide each term in $10 y = 2 x - 4$ by $10$ and simplify.

Divide each term in $10 y = 2 x - 4$ by $10$ .

$\frac{10 y}{10} = \frac{2 x}{10} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{2 x}{10} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Divide $y$ by $1$ .

$y = \frac{2 x}{10} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

$y = \frac{2 x}{10} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

$y = \frac{2 x}{10} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 x$ .

$y = \frac{2 (x)}{10} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Cancel the common factors.

Factor $2$ out of $10$ .

$y = \frac{2 x}{2 \cdot 5} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Cancel the common factor.

$y = \frac{2 x}{2 \cdot 5} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Rewrite the expression.

$y = \frac{x}{5} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

$y = \frac{x}{5} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

$y = \frac{x}{5} + \frac{- 4}{10}$

$- 14 = - 20 y - 7 x$

Cancel the common factor of $- 4$ and $10$ .

Factor $2$ out of $- 4$ .

$y = \frac{x}{5} + \frac{2 (- 2)}{10}$

$- 14 = - 20 y - 7 x$

Cancel the common factors.

Factor $2$ out of $10$ .

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

$- 14 = - 20 y - 7 x$

Cancel the common factor.

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

$- 14 = - 20 y - 7 x$

Rewrite the expression.

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

$- 14 = - 20 y - 7 x$

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

$- 14 = - 20 y - 7 x$

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

$- 14 = - 20 y - 7 x$

Move the negative in front of the fraction.

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

$- 14 = - 20 y - 7 x$

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

$- 14 = - 20 y - 7 x$

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

$- 14 = - 20 y - 7 x$

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

$- 14 = - 20 y - 7 x$

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

$- 14 = - 20 y - 7 x$

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

Replace all occurrences of $y$ in $- 14 = - 20 y - 7 x$ with $\frac{x}{5} - \frac{2}{5}$ .

$- 14 = - 20 (\frac{x}{5} - \frac{2}{5}) - 7 x$

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

Simplify the right side.

Simplify $- 20 (\frac{x}{5} - \frac{2}{5}) - 7 x$ .

Simplify each term.

Apply the distributive property.

$- 14 = - 20 \frac{x}{5} - 20 (- \frac{2}{5}) - 7 x$

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 20$ .

$- 14 = 5 (- 4) (\frac{x}{5}) - 20 (- \frac{2}{5}) - 7 x$

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

Cancel the common factor.

$- 14 = 5 \cdot (- 4 \frac{x}{5}) - 20 (- \frac{2}{5}) - 7 x$

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

Rewrite the expression.

$- 14 = - 4 x - 20 (- \frac{2}{5}) - 7 x$

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

$- 14 = - 4 x - 20 (- \frac{2}{5}) - 7 x$

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$- 14 = - 4 x - 20 (\frac{- 2}{5}) - 7 x$

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

Factor $5$ out of $- 20$ .

$- 14 = - 4 x + 5 (- 4) (\frac{- 2}{5}) - 7 x$

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

Cancel the common factor.

$- 14 = - 4 x + 5 \cdot (- 4 (\frac{- 2}{5})) - 7 x$

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

Rewrite the expression.

$- 14 = - 4 x - 4 \cdot - 2 - 7 x$

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

$- 14 = - 4 x - 4 \cdot - 2 - 7 x$

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

Multiply $- 4$ by $- 2$ .

$- 14 = - 4 x + 8 - 7 x$

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

$- 14 = - 4 x + 8 - 7 x$

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

Subtract $7 x$ from $- 4 x$ .

$- 14 = - 11 x + 8$

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

$- 14 = - 11 x + 8$

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

$- 14 = - 11 x + 8$

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

$- 14 = - 11 x + 8$

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

Solve for $x$ in $- 14 = - 11 x + 8$ .

Rewrite the equation as $- 11 x + 8 = - 14$ .

$- 11 x + 8 = - 14$

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

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

Subtract $8$ from both sides of the equation.

$- 11 x = - 14 - 8$

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

Subtract $8$ from $- 14$ .

$- 11 x = - 22$

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

$- 11 x = - 22$

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

Divide each term in $- 11 x = - 22$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 22$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 22}{- 11}$

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

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 22}{- 11}$

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

Divide $x$ by $1$ .

$x = \frac{- 22}{- 11}$

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

$x = \frac{- 22}{- 11}$

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

$x = \frac{- 22}{- 11}$

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

Simplify the right side.

Divide $- 22$ by $- 11$ .

$x = 2$

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

$x = 2$

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

$x = 2$

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

$x = 2$

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

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

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

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

$x = 2$

Simplify the right side.

Simplify $\frac{2}{5} - \frac{2}{5}$ .

Combine the numerators over the common denominator.

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

$x = 2$

Simplify the expression.

Subtract $2$ from $2$ .

$y = \frac{0}{5}$

$x = 2$

Divide $0$ by $5$ .

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

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

$(2, 0)$

The result can be shown in multiple forms.

Point Form:

$(2, 0)$

Equation Form:

$x = 2, y = 0$

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