Solve by Substitution -3x+7y=-16 , -9x+5y=16

$- 3 x + 7 y = - 16$ , $- 9 x + 5 y = 16$

Step 1

Solve for $x$ in $- 3 x + 7 y = - 16$ .

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

$- 3 x = - 16 - 7 y$

$- 9 x + 5 y = 16$

Divide each term in $- 3 x = - 16 - 7 y$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 16 - 7 y$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 16}{- 3} + \frac{- 7 y}{- 3}$

$- 9 x + 5 y = 16$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 16}{- 3} + \frac{- 7 y}{- 3}$

$- 9 x + 5 y = 16$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 3} + \frac{- 7 y}{- 3}$

$- 9 x + 5 y = 16$

$x = \frac{- 16}{- 3} + \frac{- 7 y}{- 3}$

$- 9 x + 5 y = 16$

$x = \frac{- 16}{- 3} + \frac{- 7 y}{- 3}$

$- 9 x + 5 y = 16$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{16}{3} + \frac{- 7 y}{- 3}$

$- 9 x + 5 y = 16$

Dividing two negative values results in a positive value.

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 9 x + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 9 x + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 9 x + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 9 x + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 9 x + 5 y = 16$

Step 2

Replace all occurrences of $x$ with $\frac{16}{3} + \frac{7 y}{3}$ in each equation.

Replace all occurrences of $x$ in $- 9 x + 5 y = 16$ with $\frac{16}{3} + \frac{7 y}{3}$ .

$- 9 (\frac{16}{3} + \frac{7 y}{3}) + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Simplify the left side.

Simplify $- 9 (\frac{16}{3} + \frac{7 y}{3}) + 5 y$ .

Simplify each term.

Apply the distributive property.

$- 9 (\frac{16}{3}) - 9 \frac{7 y}{3} + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

$3 (- 3) (\frac{16}{3}) - 9 \frac{7 y}{3} + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Cancel the common factor.

$3 \cdot (- 3 (\frac{16}{3})) - 9 \frac{7 y}{3} + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Rewrite the expression.

$- 3 \cdot 16 - 9 \frac{7 y}{3} + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 3 \cdot 16 - 9 \frac{7 y}{3} + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Multiply $- 3$ by $16$ .

$- 48 - 9 \frac{7 y}{3} + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

$- 48 + 3 (- 3) (\frac{7 y}{3}) + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Cancel the common factor.

$- 48 + 3 \cdot (- 3 \frac{7 y}{3}) + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Rewrite the expression.

$- 48 - 3 (7 y) + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 48 - 3 (7 y) + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Multiply $7$ by $- 3$ .

$- 48 - 21 y + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 48 - 21 y + 5 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Add $- 21 y$ and $5 y$ .

$- 48 - 16 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 48 - 16 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 48 - 16 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 48 - 16 y = 16$

$x = \frac{16}{3} + \frac{7 y}{3}$

Step 3

Solve for $y$ in $- 48 - 16 y = 16$ .

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

Add $48$ to both sides of the equation.

$- 16 y = 16 + 48$

$x = \frac{16}{3} + \frac{7 y}{3}$

Add $16$ and $48$ .

$- 16 y = 64$

$x = \frac{16}{3} + \frac{7 y}{3}$

$- 16 y = 64$

$x = \frac{16}{3} + \frac{7 y}{3}$

Divide each term in $- 16 y = 64$ by $- 16$ and simplify.

Divide each term in $- 16 y = 64$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{64}{- 16}$

$x = \frac{16}{3} + \frac{7 y}{3}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{64}{- 16}$

$x = \frac{16}{3} + \frac{7 y}{3}$

Divide $y$ by $1$ .

$y = \frac{64}{- 16}$

$x = \frac{16}{3} + \frac{7 y}{3}$

$y = \frac{64}{- 16}$

$x = \frac{16}{3} + \frac{7 y}{3}$

$y = \frac{64}{- 16}$

$x = \frac{16}{3} + \frac{7 y}{3}$

Simplify the right side.

Divide $64$ by $- 16$ .

$y = - 4$

$x = \frac{16}{3} + \frac{7 y}{3}$

$y = - 4$

$x = \frac{16}{3} + \frac{7 y}{3}$

$y = - 4$

$x = \frac{16}{3} + \frac{7 y}{3}$

$y = - 4$

$x = \frac{16}{3} + \frac{7 y}{3}$

Step 4

Replace all occurrences of $y$ with $- 4$ in each equation.

Replace all occurrences of $y$ in $x = \frac{16}{3} + \frac{7 y}{3}$ with $- 4$ .

$x = \frac{16}{3} + \frac{7 (- 4)}{3}$

$y = - 4$

Simplify the right side.

Simplify $\frac{16}{3} + \frac{7 (- 4)}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{16 + 7 (- 4)}{3}$

$y = - 4$

Simplify the expression.

Multiply $7$ by $- 4$ .

$x = \frac{16 - 28}{3}$

$y = - 4$

Subtract $28$ from $16$ .

$x = \frac{- 12}{3}$

$y = - 4$

Divide $- 12$ by $3$ .

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

$x = - 4$

$y = - 4$

Step 5

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

$(- 4, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, - 4)$

Equation Form:

$x = - 4, y = - 4$

Step 7

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