Solve the System of Equations 0=-2y+10-6x 14-22y=18x

$0 = - 2 y + 10 - 6 x$ $14 - 22 y = 18 x$

Solve for $y$ in $14 - 22 y = 18 x$ .

Subtract $14$ from both sides of the equation.

$- 22 y = 18 x - 14$

$0 = - 2 y + 10 - 6 x$

Divide each term in $- 22 y = 18 x - 14$ by $- 22$ and simplify.

Divide each term in $- 22 y = 18 x - 14$ by $- 22$ .

$\frac{- 22 y}{- 22} = \frac{18 x}{- 22} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Simplify the left side.

Cancel the common factor of $- 22$ .

Cancel the common factor.

$\frac{- 22 y}{- 22} = \frac{18 x}{- 22} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Divide $y$ by $1$ .

$y = \frac{18 x}{- 22} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

$y = \frac{18 x}{- 22} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

$y = \frac{18 x}{- 22} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Simplify the right side.

Simplify each term.

Cancel the common factor of $18$ and $- 22$ .

Factor $2$ out of $18 x$ .

$y = \frac{2 (9 x)}{- 22} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Cancel the common factors.

Factor $2$ out of $- 22$ .

$y = \frac{2 (9 x)}{2 (- 11)} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Cancel the common factor.

$y = \frac{2 (9 x)}{2 \cdot - 11} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Rewrite the expression.

$y = \frac{9 x}{- 11} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

$y = \frac{9 x}{- 11} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

$y = \frac{9 x}{- 11} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Move the negative in front of the fraction.

$y = - \frac{9 x}{11} + \frac{- 14}{- 22}$

$0 = - 2 y + 10 - 6 x$

Cancel the common factor of $- 14$ and $- 22$ .

Factor $- 2$ out of $- 14$ .

$y = - \frac{9 x}{11} + \frac{- 2 \cdot 7}{- 22}$

$0 = - 2 y + 10 - 6 x$

Cancel the common factors.

Factor $- 2$ out of $- 22$ .

$y = - \frac{9 x}{11} + \frac{- 2 \cdot 7}{- 2 \cdot 11}$

$0 = - 2 y + 10 - 6 x$

Cancel the common factor.

$y = - \frac{9 x}{11} + \frac{- 2 \cdot 7}{- 2 \cdot 11}$

$0 = - 2 y + 10 - 6 x$

Rewrite the expression.

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - 2 y + 10 - 6 x$

Replace all occurrences of $y$ with $- \frac{9 x}{11} + \frac{7}{11}$ in each equation.

Replace all occurrences of $y$ in $0 = - 2 y + 10 - 6 x$ with $- \frac{9 x}{11} + \frac{7}{11}$ .

$0 = - 2 (- \frac{9 x}{11} + \frac{7}{11}) + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify the right side.

Simplify $- 2 (- \frac{9 x}{11} + \frac{7}{11}) + 10 - 6 x$ .

Simplify each term.

Apply the distributive property.

$0 = - 2 (- \frac{9 x}{11}) - 2 (\frac{7}{11}) + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $- 2 (- \frac{9 x}{11})$ .

Multiply $- 1$ by $- 2$ .

$0 = 2 (\frac{9 x}{11}) - 2 (\frac{7}{11}) + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Combine $2$ and $\frac{9 x}{11}$ .

$0 = \frac{2 (9 x)}{11} - 2 (\frac{7}{11}) + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $9$ by $2$ .

$0 = \frac{18 x}{11} - 2 (\frac{7}{11}) + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{18 x}{11} - 2 (\frac{7}{11}) + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $- 2 (\frac{7}{11})$ .

Combine $- 2$ and $\frac{7}{11}$ .

$0 = \frac{18 x}{11} + \frac{- 2 \cdot 7}{11} + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $- 2$ by $7$ .

$0 = \frac{18 x}{11} + \frac{- 14}{11} + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{18 x}{11} + \frac{- 14}{11} + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Move the negative in front of the fraction.

$0 = \frac{18 x}{11} - \frac{14}{11} + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{18 x}{11} - \frac{14}{11} + 10 - 6 x$

$y = - \frac{9 x}{11} + \frac{7}{11}$

To write $- 6 x$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$0 = \frac{18 x}{11} - 6 x \cdot \frac{11}{11} - \frac{14}{11} + 10$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Combine $- 6 x$ and $\frac{11}{11}$ .

$0 = \frac{18 x}{11} + \frac{- 6 x \cdot 11}{11} - \frac{14}{11} + 10$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Combine the numerators over the common denominator.

$0 = \frac{18 x - 6 x \cdot 11}{11} - \frac{14}{11} + 10$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Combine the numerators over the common denominator.

$0 = 10 + \frac{18 x - 6 x \cdot 11 - 14}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $11$ by $- 6$ .

$0 = 10 + \frac{18 x - 66 x - 14}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Subtract $66 x$ from $18 x$ .

$0 = 10 + \frac{- 48 x - 14}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $2$ out of $- 48 x - 14$ .

Factor $2$ out of $- 48 x$ .

$0 = 10 + \frac{2 (- 24 x) - 14}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $2$ out of $- 14$ .

$0 = 10 + \frac{2 (- 24 x) + 2 (- 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $2$ out of $2 (- 24 x) + 2 (- 7)$ .

$0 = 10 + \frac{2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = 10 + \frac{2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$0 = 10 \cdot \frac{11}{11} + \frac{2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify terms.

Combine $10$ and $\frac{11}{11}$ .

$0 = \frac{10 \cdot 11}{11} + \frac{2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Combine the numerators over the common denominator.

$0 = \frac{10 \cdot 11 + 2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{10 \cdot 11 + 2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify the numerator.

Factor $2$ out of $10 \cdot 11 + 2 (- 24 x - 7)$ .

Factor $2$ out of $10 \cdot 11$ .

$0 = \frac{2 (5 \cdot 11) + 2 (- 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $2$ out of $2 (5 \cdot 11) + 2 (- 24 x - 7)$ .

$0 = \frac{2 (5 \cdot 11 - 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{2 (5 \cdot 11 - 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $5$ by $11$ .

$0 = \frac{2 (55 - 24 x - 7)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Subtract $7$ from $55$ .

$0 = \frac{2 (- 24 x + 48)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $24$ out of $- 24 x + 48$ .

Factor $24$ out of $- 24 x$ .

$0 = \frac{2 (24 (- x) + 48)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $24$ out of $48$ .

$0 = \frac{2 (24 (- x) + 24 (2))}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $24$ out of $24 (- x) + 24 (2)$ .

$0 = \frac{2 (24 (- x + 2))}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{2 \cdot (24 (- x + 2))}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Multiply $2$ by $24$ .

$0 = \frac{48 (- x + 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = \frac{48 (- x + 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$0 = \frac{48 (- (x) + 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Rewrite $2$ as $- 1 (- 2)$ .

$0 = \frac{48 (- (x) - 1 \cdot - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Factor $- 1$ out of $- (x) - 1 (- 2)$ .

$0 = \frac{48 (- (x - 2))}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify the expression.

Rewrite $- (x - 2)$ as $- 1 (x - 2)$ .

$0 = \frac{48 (- 1 (x - 2))}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Move the negative in front of the fraction.

$0 = - \frac{48 (x - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - \frac{48 (x - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - \frac{48 (x - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - \frac{48 (x - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - \frac{48 (x - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$0 = - \frac{48 (x - 2)}{11}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Solve for $x$ in $0 = - \frac{48 (x - 2)}{11}$ .

Set the numerator equal to zero.

$48 (x - 2) = 0$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Solve the equation for $x$ .

Divide each term in $48 (x - 2) = 0$ by $48$ and simplify.

Divide each term in $48 (x - 2) = 0$ by $48$ .

$\frac{48 (x - 2)}{48} = \frac{0}{48}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify the left side.

Cancel the common factor of $48$ .

Cancel the common factor.

$\frac{48 (x - 2)}{48} = \frac{0}{48}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Divide $x - 2$ by $1$ .

$x - 2 = \frac{0}{48}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$x - 2 = \frac{0}{48}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$x - 2 = \frac{0}{48}$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Simplify the right side.

Divide $0$ by $48$ .

$x - 2 = 0$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$x - 2 = 0$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$x - 2 = 0$

$y = - \frac{9 x}{11} + \frac{7}{11}$

Add $2$ to both sides of the equation.

$x = 2$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$x = 2$

$y = - \frac{9 x}{11} + \frac{7}{11}$

$x = 2$

$y = - \frac{9 x}{11} + \frac{7}{11}$

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

Replace all occurrences of $x$ in $y = - \frac{9 x}{11} + \frac{7}{11}$ with $2$ .

$y = - \frac{9 (2)}{11} + \frac{7}{11}$

$x = 2$

Simplify the right side.

Simplify $- \frac{9 (2)}{11} + \frac{7}{11}$ .

Combine the numerators over the common denominator.

$y = \frac{- 9 \cdot 2 + 7}{11}$

$x = 2$

Simplify the expression.

Multiply $- 9$ by $2$ .

$y = \frac{- 18 + 7}{11}$

$x = 2$

Add $- 18$ and $7$ .

$y = \frac{- 11}{11}$

$x = 2$

Divide $- 11$ by $11$ .

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

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

$(2, - 1)$

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

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