Solve by Substitution 13x-2y=70 2x-2y=4

$13 x - 2 y = 70$ $2 x - 2 y = 4$

Step 1

Solve for $x$ in $13 x - 2 y = 70$ .

Add $2 y$ to both sides of the equation.

$13 x = 70 + 2 y$

$2 x - 2 y = 4$

Divide each term in $13 x = 70 + 2 y$ by $13$ and simplify.

Divide each term in $13 x = 70 + 2 y$ by $13$ .

$\frac{13 x}{13} = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

Divide $x$ by $1$ .

$x = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$2 x - 2 y = 4$

Step 2

Replace all occurrences of $x$ with $\frac{70}{13} + \frac{2 y}{13}$ in each equation.

Replace all occurrences of $x$ in $2 x - 2 y = 4$ with $\frac{70}{13} + \frac{2 y}{13}$ .

$2 (\frac{70}{13} + \frac{2 y}{13}) - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Simplify the left side.

Simplify $2 (\frac{70}{13} + \frac{2 y}{13}) - 2 y$ .

Simplify each term.

Apply the distributive property.

$2 (\frac{70}{13}) + 2 (\frac{2 y}{13}) - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Multiply $2 (\frac{70}{13})$ .

Combine $2$ and $\frac{70}{13}$ .

$\frac{2 \cdot 70}{13} + 2 (\frac{2 y}{13}) - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Multiply $2$ by $70$ .

$\frac{140}{13} + 2 (\frac{2 y}{13}) - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{140}{13} + 2 (\frac{2 y}{13}) - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Multiply $2 \frac{2 y}{13}$ .

Combine $2$ and $\frac{2 y}{13}$ .

$\frac{140}{13} + \frac{2 (2 y)}{13} - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Multiply $2$ by $2$ .

$\frac{140}{13} + \frac{4 y}{13} - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{140}{13} + \frac{4 y}{13} - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{140}{13} + \frac{4 y}{13} - 2 y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{140}{13} + \frac{4 y}{13} - 2 y \cdot \frac{13}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Combine $- 2 y$ and $\frac{13}{13}$ .

$\frac{140}{13} + \frac{4 y}{13} + \frac{- 2 y \cdot 13}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Combine the numerators over the common denominator.

$\frac{140}{13} + \frac{4 y - 2 y \cdot 13}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Combine the numerators over the common denominator.

$\frac{140 + 4 y - 2 y \cdot 13}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Multiply $13$ by $- 2$ .

$\frac{140 + 4 y - 26 y}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Subtract $26 y$ from $4 y$ .

$\frac{140 - 22 y}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Factor $2$ out of $140 - 22 y$ .

Factor $2$ out of $140$ .

$\frac{2 (70) - 22 y}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

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

$\frac{2 (70) + 2 (- 11 y)}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Factor $2$ out of $2 (70) + 2 (- 11 y)$ .

$\frac{2 (70 - 11 y)}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{2 (70 - 11 y)}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{2 (70 - 11 y)}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{2 (70 - 11 y)}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$\frac{2 (70 - 11 y)}{13} = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Step 3

Solve for $y$ in $\frac{2 (70 - 11 y)}{13} = 4$ .

Multiply both sides by $13$ .

$\frac{2 (70 - 11 y)}{13} \cdot 13 = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Simplify.

Simplify the left side.

Simplify $\frac{2 (70 - 11 y)}{13} \cdot 13$ .

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{2 (70 - 11 y)}{13} \cdot 13 = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Rewrite the expression.

$2 (70 - 11 y) = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

$2 (70 - 11 y) = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Apply the distributive property.

$2 \cdot 70 + 2 (- 11 y) = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Simplify the expression.

Multiply $2$ by $70$ .

$140 + 2 (- 11 y) = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Multiply $- 11$ by $2$ .

$140 - 22 y = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Reorder $140$ and $- 22 y$ .

$- 22 y + 140 = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

$- 22 y + 140 = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

$- 22 y + 140 = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

$- 22 y + 140 = 4 \cdot 13$

$x = \frac{70}{13} + \frac{2 y}{13}$

Simplify the right side.

Multiply $4$ by $13$ .

$- 22 y + 140 = 52$

$x = \frac{70}{13} + \frac{2 y}{13}$

$- 22 y + 140 = 52$

$x = \frac{70}{13} + \frac{2 y}{13}$

$- 22 y + 140 = 52$

$x = \frac{70}{13} + \frac{2 y}{13}$

Solve for $y$ .

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

Subtract $140$ from both sides of the equation.

$- 22 y = 52 - 140$

$x = \frac{70}{13} + \frac{2 y}{13}$

Subtract $140$ from $52$ .

$- 22 y = - 88$

$x = \frac{70}{13} + \frac{2 y}{13}$

$- 22 y = - 88$

$x = \frac{70}{13} + \frac{2 y}{13}$

Divide each term in $- 22 y = - 88$ by $- 22$ and simplify.

Divide each term in $- 22 y = - 88$ by $- 22$ .

$\frac{- 22 y}{- 22} = \frac{- 88}{- 22}$

$x = \frac{70}{13} + \frac{2 y}{13}$

Simplify the left side.

Cancel the common factor of $- 22$ .

Cancel the common factor.

$\frac{- 22 y}{- 22} = \frac{- 88}{- 22}$

$x = \frac{70}{13} + \frac{2 y}{13}$

Divide $y$ by $1$ .

$y = \frac{- 88}{- 22}$

$x = \frac{70}{13} + \frac{2 y}{13}$

$y = \frac{- 88}{- 22}$

$x = \frac{70}{13} + \frac{2 y}{13}$

$y = \frac{- 88}{- 22}$

$x = \frac{70}{13} + \frac{2 y}{13}$

Simplify the right side.

Divide $- 88$ by $- 22$ .

$y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

$y = 4$

$x = \frac{70}{13} + \frac{2 y}{13}$

Step 4

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

Replace all occurrences of $y$ in $x = \frac{70}{13} + \frac{2 y}{13}$ with $4$ .

$x = \frac{70}{13} + \frac{2 (4)}{13}$

$y = 4$

Simplify the right side.

Simplify $\frac{70}{13} + \frac{2 (4)}{13}$ .

Combine the numerators over the common denominator.

$x = \frac{70 + 2 (4)}{13}$

$y = 4$

Simplify the expression.

Multiply $2$ by $4$ .

$x = \frac{70 + 8}{13}$

$y = 4$

Add $70$ and $8$ .

$x = \frac{78}{13}$

$y = 4$

Divide $78$ by $13$ .

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

Step 5

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

$(6, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, 4)$

Equation Form:

$x = 6, y = 4$

Step 7

Solve by Substitution 13x-2y=70 2x-2y=4

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