Solve the System of Equations 4x+2y=-14 and 7x-y=16

$4 x + 2 y = - 14$ and $7 x - y = 16$

Solve for $x$ in $4 x + 2 y = - 14$ .

Subtract $2 y$ from both sides of the equation.

$4 x = - 14 - 2 y$

$7 x - y = 16$

Divide each term in $4 x = - 14 - 2 y$ by $4$ and simplify.

Divide each term in $4 x = - 14 - 2 y$ by $4$ .

$\frac{4 x}{4} = \frac{- 14}{4} + \frac{- 2 y}{4}$

$7 x - y = 16$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 14}{4} + \frac{- 2 y}{4}$

$7 x - y = 16$

Divide $x$ by $1$ .

$x = \frac{- 14}{4} + \frac{- 2 y}{4}$

$7 x - y = 16$

$x = \frac{- 14}{4} + \frac{- 2 y}{4}$

$7 x - y = 16$

$x = \frac{- 14}{4} + \frac{- 2 y}{4}$

$7 x - y = 16$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 14$ and $4$ .

Factor $2$ out of $- 14$ .

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

$7 x - y = 16$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 7}{2 \cdot 2} + \frac{- 2 y}{4}$

$7 x - y = 16$

Cancel the common factor.

$x = \frac{2 \cdot - 7}{2 \cdot 2} + \frac{- 2 y}{4}$

$7 x - y = 16$

Rewrite the expression.

$x = \frac{- 7}{2} + \frac{- 2 y}{4}$

$7 x - y = 16$

$x = \frac{- 7}{2} + \frac{- 2 y}{4}$

$7 x - y = 16$

$x = \frac{- 7}{2} + \frac{- 2 y}{4}$

$7 x - y = 16$

Move the negative in front of the fraction.

$x = - \frac{7}{2} + \frac{- 2 y}{4}$

$7 x - y = 16$

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 y$ .

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

$7 x - y = 16$

Cancel the common factors.

Factor $2$ out of $4$ .

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

$7 x - y = 16$

Cancel the common factor.

$x = - \frac{7}{2} + \frac{2 (- y)}{2 \cdot 2}$

$7 x - y = 16$

Rewrite the expression.

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

$7 x - y = 16$

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

$7 x - y = 16$

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

$7 x - y = 16$

Move the negative in front of the fraction.

$x = - \frac{7}{2} - \frac{y}{2}$

$7 x - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$7 x - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$7 x - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$7 x - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$7 x - y = 16$

Replace all occurrences of $x$ with $- \frac{7}{2} - \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $7 x - y = 16$ with $- \frac{7}{2} - \frac{y}{2}$ .

$7 (- \frac{7}{2} - \frac{y}{2}) - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Simplify the left side.

Simplify $7 (- \frac{7}{2} - \frac{y}{2}) - y$ .

Simplify each term.

Apply the distributive property.

$7 (- \frac{7}{2}) + 7 (- \frac{y}{2}) - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

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

Multiply $- 1$ by $7$ .

$- 7 (\frac{7}{2}) + 7 (- \frac{y}{2}) - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

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

$\frac{- 7 \cdot 7}{2} + 7 (- \frac{y}{2}) - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Multiply $- 7$ by $7$ .

$\frac{- 49}{2} + 7 (- \frac{y}{2}) - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$\frac{- 49}{2} + 7 (- \frac{y}{2}) - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

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

Multiply $- 1$ by $7$ .

$\frac{- 49}{2} - 7 \frac{y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

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

$\frac{- 49}{2} + \frac{- 7 y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$\frac{- 49}{2} + \frac{- 7 y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{49}{2} + \frac{- 7 y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Move the negative in front of the fraction.

$- \frac{49}{2} - \frac{7 y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$- \frac{49}{2} - \frac{7 y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$- \frac{49}{2} - \frac{7 y}{2} - y = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

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

$- \frac{49}{2} - \frac{7 y}{2} - y \cdot \frac{2}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

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

$- \frac{49}{2} - \frac{7 y}{2} + \frac{- y \cdot 2}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Combine the numerators over the common denominator.

$- \frac{49}{2} + \frac{- 7 y - y \cdot 2}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Combine the numerators over the common denominator.

$\frac{- 49 - 7 y - y \cdot 2}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Multiply $2$ by $- 1$ .

$\frac{- 49 - 7 y - 2 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Subtract $2 y$ from $- 7 y$ .

$\frac{- 49 - 9 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{- 1 \cdot 49 - 9 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Factor $- 1$ out of $- 9 y$ .

$\frac{- 1 \cdot 49 - (9 y)}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Factor $- 1$ out of $- 1 (49) - (9 y)$ .

$\frac{- 1 (49 + 9 y)}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Move the negative in front of the fraction.

$- \frac{49 + 9 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$- \frac{49 + 9 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$- \frac{49 + 9 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$- \frac{49 + 9 y}{2} = 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Solve for $y$ in $- \frac{49 + 9 y}{2} = 16$ .

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{49 + 9 y}{2}) = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{49 + 9 y}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{49 + 9 y}{2}$ into the numerator.

$- 2 \frac{- (49 + 9 y)}{2} = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (49 + 9 y)}{2}) = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Cancel the common factor.

$2 \cdot (- 1 \frac{- (49 + 9 y)}{2}) = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Rewrite the expression.

$49 + 9 y = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$49 + 9 y = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (49 + 9 y) = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Multiply $49 + 9 y$ by $1$ .

$49 + 9 y = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$49 + 9 y = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$49 + 9 y = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

$49 + 9 y = - 2 \cdot 16$

$x = - \frac{7}{2} - \frac{y}{2}$

Simplify the right side.

Multiply $- 2$ by $16$ .

$49 + 9 y = - 32$

$x = - \frac{7}{2} - \frac{y}{2}$

$49 + 9 y = - 32$

$x = - \frac{7}{2} - \frac{y}{2}$

$49 + 9 y = - 32$

$x = - \frac{7}{2} - \frac{y}{2}$

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

Subtract $49$ from both sides of the equation.

$9 y = - 32 - 49$

$x = - \frac{7}{2} - \frac{y}{2}$

Subtract $49$ from $- 32$ .

$9 y = - 81$

$x = - \frac{7}{2} - \frac{y}{2}$

$9 y = - 81$

$x = - \frac{7}{2} - \frac{y}{2}$

Divide each term in $9 y = - 81$ by $9$ and simplify.

Divide each term in $9 y = - 81$ by $9$ .

$\frac{9 y}{9} = \frac{- 81}{9}$

$x = - \frac{7}{2} - \frac{y}{2}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 81}{9}$

$x = - \frac{7}{2} - \frac{y}{2}$

Divide $y$ by $1$ .

$y = \frac{- 81}{9}$

$x = - \frac{7}{2} - \frac{y}{2}$

$y = \frac{- 81}{9}$

$x = - \frac{7}{2} - \frac{y}{2}$

$y = \frac{- 81}{9}$

$x = - \frac{7}{2} - \frac{y}{2}$

Simplify the right side.

Divide $- 81$ by $9$ .

$y = - 9$

$x = - \frac{7}{2} - \frac{y}{2}$

$y = - 9$

$x = - \frac{7}{2} - \frac{y}{2}$

$y = - 9$

$x = - \frac{7}{2} - \frac{y}{2}$

$y = - 9$

$x = - \frac{7}{2} - \frac{y}{2}$

Replace all occurrences of $y$ with $- 9$ in each equation.

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

$x = - \frac{7}{2} - \frac{- 9}{2}$

$y = - 9$

Simplify the right side.

Simplify $- \frac{7}{2} - \frac{- 9}{2}$ .

Combine the numerators over the common denominator.

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

$y = - 9$

Simplify the expression.

Add $- 7$ and $9$ .

$x = \frac{2}{2}$

$y = - 9$

Divide $2$ by $2$ .

$x = 1$

$y = - 9$

$x = 1$

$y = - 9$

$x = 1$

$y = - 9$

$x = 1$

$y = - 9$

$x = 1$

$y = - 9$

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

$(1, - 9)$

The result can be shown in multiple forms.

Point Form:

$(1, - 9)$

Equation Form:

$x = 1, y = - 9$

Solve the System of Equations 4x+2y=-14 and 7x-y=16

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