Solve the System of Equations x-3y=5 and 8x-7y=6

$x - 3 y = 5$ and $8 x - 7 y = 6$

Step 1

Add $3 y$ to both sides of the equation.

$x = 5 + 3 y$

$8 x - 7 y = 6$

Step 2

Replace all occurrences of $x$ with $5 + 3 y$ in each equation.

Replace all occurrences of $x$ in $8 x - 7 y = 6$ with $5 + 3 y$ .

$8 (5 + 3 y) - 7 y = 6$

$x = 5 + 3 y$

Simplify the left side.

Simplify $8 (5 + 3 y) - 7 y$ .

Simplify each term.

Apply the distributive property.

$8 \cdot 5 + 8 (3 y) - 7 y = 6$

$x = 5 + 3 y$

Multiply $8$ by $5$ .

$40 + 8 (3 y) - 7 y = 6$

$x = 5 + 3 y$

Multiply $3$ by $8$ .

$40 + 24 y - 7 y = 6$

$x = 5 + 3 y$

$40 + 24 y - 7 y = 6$

$x = 5 + 3 y$

Subtract $7 y$ from $24 y$ .

$40 + 17 y = 6$

$x = 5 + 3 y$

$40 + 17 y = 6$

$x = 5 + 3 y$

$40 + 17 y = 6$

$x = 5 + 3 y$

$40 + 17 y = 6$

$x = 5 + 3 y$

Step 3

Solve for $y$ in $40 + 17 y = 6$ .

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

Subtract $40$ from both sides of the equation.

$17 y = 6 - 40$

$x = 5 + 3 y$

Subtract $40$ from $6$ .

$17 y = - 34$

$x = 5 + 3 y$

$17 y = - 34$

$x = 5 + 3 y$

Divide each term in $17 y = - 34$ by $17$ and simplify.

Divide each term in $17 y = - 34$ by $17$ .

$\frac{17 y}{17} = \frac{- 34}{17}$

$x = 5 + 3 y$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 y}{17} = \frac{- 34}{17}$

$x = 5 + 3 y$

Divide $y$ by $1$ .

$y = \frac{- 34}{17}$

$x = 5 + 3 y$

$y = \frac{- 34}{17}$

$x = 5 + 3 y$

$y = \frac{- 34}{17}$

$x = 5 + 3 y$

Simplify the right side.

Divide $- 34$ by $17$ .

$y = - 2$

$x = 5 + 3 y$

$y = - 2$

$x = 5 + 3 y$

$y = - 2$

$x = 5 + 3 y$

$y = - 2$

$x = 5 + 3 y$

Step 4

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $x = 5 + 3 y$ with $- 2$ .

$x = 5 + 3 (- 2)$

$y = - 2$

Simplify the right side.

Simplify $5 + 3 (- 2)$ .

Multiply $3$ by $- 2$ .

$x = 5 - 6$

$y = - 2$

Subtract $6$ from $5$ .

$x = - 1$

$y = - 2$

$x = - 1$

$y = - 2$

$x = - 1$

$y = - 2$

$x = - 1$

$y = - 2$

Step 5

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

$(- 1, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 2)$

Equation Form:

$x = - 1, y = - 2$

Step 7

Solve the System of Equations x-3y=5 and 8x-7y=6

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