Solve the System of Equations -8x+3y=-17 and 3x-y=7

$- 8 x + 3 y = - 17$ and $3 x - y = 7$

Step 1

Solve for $x$ in $- 8 x + 3 y = - 17$ .

Subtract $3 y$ from both sides of the equation.

$- 8 x = - 17 - 3 y$

$3 x - y = 7$

Divide each term in $- 8 x = - 17 - 3 y$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 17 - 3 y$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 17}{- 8} + \frac{- 3 y}{- 8}$

$3 x - y = 7$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 17}{- 8} + \frac{- 3 y}{- 8}$

$3 x - y = 7$

Divide $x$ by $1$ .

$x = \frac{- 17}{- 8} + \frac{- 3 y}{- 8}$

$3 x - y = 7$

$x = \frac{- 17}{- 8} + \frac{- 3 y}{- 8}$

$3 x - y = 7$

$x = \frac{- 17}{- 8} + \frac{- 3 y}{- 8}$

$3 x - y = 7$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{17}{8} + \frac{- 3 y}{- 8}$

$3 x - y = 7$

Dividing two negative values results in a positive value.

$x = \frac{17}{8} + \frac{3 y}{8}$

$3 x - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$3 x - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$3 x - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$3 x - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$3 x - y = 7$

Step 2

Replace all occurrences of $x$ with $\frac{17}{8} + \frac{3 y}{8}$ in each equation.

Replace all occurrences of $x$ in $3 x - y = 7$ with $\frac{17}{8} + \frac{3 y}{8}$ .

$3 (\frac{17}{8} + \frac{3 y}{8}) - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Simplify the left side.

Simplify $3 (\frac{17}{8} + \frac{3 y}{8}) - y$ .

Simplify each term.

Apply the distributive property.

$3 (\frac{17}{8}) + 3 (\frac{3 y}{8}) - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Multiply $3 (\frac{17}{8})$ .

Combine $3$ and $\frac{17}{8}$ .

$\frac{3 \cdot 17}{8} + 3 (\frac{3 y}{8}) - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Multiply $3$ by $17$ .

$\frac{51}{8} + 3 (\frac{3 y}{8}) - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$\frac{51}{8} + 3 (\frac{3 y}{8}) - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Multiply $3 \frac{3 y}{8}$ .

Combine $3$ and $\frac{3 y}{8}$ .

$\frac{51}{8} + \frac{3 (3 y)}{8} - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Multiply $3$ by $3$ .

$\frac{51}{8} + \frac{9 y}{8} - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$\frac{51}{8} + \frac{9 y}{8} - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$\frac{51}{8} + \frac{9 y}{8} - y = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

To write $- y$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{51}{8} + \frac{9 y}{8} - y \cdot \frac{8}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Combine $- y$ and $\frac{8}{8}$ .

$\frac{51}{8} + \frac{9 y}{8} + \frac{- y \cdot 8}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Combine the numerators over the common denominator.

$\frac{51}{8} + \frac{9 y - y \cdot 8}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Combine the numerators over the common denominator.

$\frac{51 + 9 y - y \cdot 8}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Multiply $8$ by $- 1$ .

$\frac{51 + 9 y - 8 y}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Subtract $8 y$ from $9 y$ .

$\frac{51 + y}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$\frac{51 + y}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$\frac{51 + y}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$\frac{51 + y}{8} = 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Step 3

Solve for $y$ in $\frac{51 + y}{8} = 7$ .

Multiply both sides of the equation by $8$ .

$8 (\frac{51 + y}{8}) = 8 \cdot 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 (\frac{51 + y}{8}) = 8 \cdot 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Rewrite the expression.

$51 + y = 8 \cdot 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$51 + y = 8 \cdot 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

$51 + y = 8 \cdot 7$

$x = \frac{17}{8} + \frac{3 y}{8}$

Simplify the right side.

Multiply $8$ by $7$ .

$51 + y = 56$

$x = \frac{17}{8} + \frac{3 y}{8}$

$51 + y = 56$

$x = \frac{17}{8} + \frac{3 y}{8}$

$51 + y = 56$

$x = \frac{17}{8} + \frac{3 y}{8}$

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

Subtract $51$ from both sides of the equation.

$y = 56 - 51$

$x = \frac{17}{8} + \frac{3 y}{8}$

Subtract $51$ from $56$ .

$y = 5$

$x = \frac{17}{8} + \frac{3 y}{8}$

$y = 5$

$x = \frac{17}{8} + \frac{3 y}{8}$

$y = 5$

$x = \frac{17}{8} + \frac{3 y}{8}$

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

Replace all occurrences of $y$ in $x = \frac{17}{8} + \frac{3 y}{8}$ with $5$ .

$x = \frac{17}{8} + \frac{3 (5)}{8}$

$y = 5$

Simplify the right side.

Simplify $\frac{17}{8} + \frac{3 (5)}{8}$ .

Combine the numerators over the common denominator.

$x = \frac{17 + 3 (5)}{8}$

$y = 5$

Simplify the expression.

Multiply $3$ by $5$ .

$x = \frac{17 + 15}{8}$

$y = 5$

Add $17$ and $15$ .

$x = \frac{32}{8}$

$y = 5$

Divide $32$ by $8$ .

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

Step 5

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

$(4, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 5)$

Equation Form:

$x = 4, y = 5$

Step 7

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