Solve by Substitution 3x-2y=5 , 4x-5y=30

$3 x - 2 y = 5$ , $4 x - 5 y = 30$

Step 1

Solve for $x$ in $3 x - 2 y = 5$ .

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

$3 x = 5 + 2 y$

$4 x - 5 y = 30$

Divide each term in $3 x = 5 + 2 y$ by $3$ and simplify.

Divide each term in $3 x = 5 + 2 y$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

Divide $x$ by $1$ .

$x = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$4 x - 5 y = 30$

Step 2

Replace all occurrences of $x$ with $\frac{5}{3} + \frac{2 y}{3}$ in each equation.

Replace all occurrences of $x$ in $4 x - 5 y = 30$ with $\frac{5}{3} + \frac{2 y}{3}$ .

$4 (\frac{5}{3} + \frac{2 y}{3}) - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Simplify the left side.

Simplify $4 (\frac{5}{3} + \frac{2 y}{3}) - 5 y$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{5}{3}) + 4 (\frac{2 y}{3}) - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Multiply $4 (\frac{5}{3})$ .

Combine $4$ and $\frac{5}{3}$ .

$\frac{4 \cdot 5}{3} + 4 (\frac{2 y}{3}) - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Multiply $4$ by $5$ .

$\frac{20}{3} + 4 (\frac{2 y}{3}) - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$\frac{20}{3} + 4 (\frac{2 y}{3}) - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Multiply $4 \frac{2 y}{3}$ .

Combine $4$ and $\frac{2 y}{3}$ .

$\frac{20}{3} + \frac{4 (2 y)}{3} - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Multiply $2$ by $4$ .

$\frac{20}{3} + \frac{8 y}{3} - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$\frac{20}{3} + \frac{8 y}{3} - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$\frac{20}{3} + \frac{8 y}{3} - 5 y = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

To write $- 5 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{20}{3} + \frac{8 y}{3} - 5 y \cdot \frac{3}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Combine $- 5 y$ and $\frac{3}{3}$ .

$\frac{20}{3} + \frac{8 y}{3} + \frac{- 5 y \cdot 3}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Combine the numerators over the common denominator.

$\frac{20}{3} + \frac{8 y - 5 y \cdot 3}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Combine the numerators over the common denominator.

$\frac{20 + 8 y - 5 y \cdot 3}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Multiply $3$ by $- 5$ .

$\frac{20 + 8 y - 15 y}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Subtract $15 y$ from $8 y$ .

$\frac{20 - 7 y}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$\frac{20 - 7 y}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$\frac{20 - 7 y}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

$\frac{20 - 7 y}{3} = 30$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 3

Solve for $y$ in $\frac{20 - 7 y}{3} = 30$ .

Multiply both sides by $3$ .

$\frac{20 - 7 y}{3} \cdot 3 = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

Simplify.

Simplify the left side.

Simplify $\frac{20 - 7 y}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{20 - 7 y}{3} \cdot 3 = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

Rewrite the expression.

$20 - 7 y = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

$20 - 7 y = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

Reorder $20$ and $- 7 y$ .

$- 7 y + 20 = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

$- 7 y + 20 = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

$- 7 y + 20 = 30 \cdot 3$

$x = \frac{5}{3} + \frac{2 y}{3}$

Simplify the right side.

Multiply $30$ by $3$ .

$- 7 y + 20 = 90$

$x = \frac{5}{3} + \frac{2 y}{3}$

$- 7 y + 20 = 90$

$x = \frac{5}{3} + \frac{2 y}{3}$

$- 7 y + 20 = 90$

$x = \frac{5}{3} + \frac{2 y}{3}$

Solve for $y$ .

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

Subtract $20$ from both sides of the equation.

$- 7 y = 90 - 20$

$x = \frac{5}{3} + \frac{2 y}{3}$

Subtract $20$ from $90$ .

$- 7 y = 70$

$x = \frac{5}{3} + \frac{2 y}{3}$

$- 7 y = 70$

$x = \frac{5}{3} + \frac{2 y}{3}$

Divide each term in $- 7 y = 70$ by $- 7$ and simplify.

Divide each term in $- 7 y = 70$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{70}{- 7}$

$x = \frac{5}{3} + \frac{2 y}{3}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{70}{- 7}$

$x = \frac{5}{3} + \frac{2 y}{3}$

Divide $y$ by $1$ .

$y = \frac{70}{- 7}$

$x = \frac{5}{3} + \frac{2 y}{3}$

$y = \frac{70}{- 7}$

$x = \frac{5}{3} + \frac{2 y}{3}$

$y = \frac{70}{- 7}$

$x = \frac{5}{3} + \frac{2 y}{3}$

Simplify the right side.

Divide $70$ by $- 7$ .

$y = - 10$

$x = \frac{5}{3} + \frac{2 y}{3}$

$y = - 10$

$x = \frac{5}{3} + \frac{2 y}{3}$

$y = - 10$

$x = \frac{5}{3} + \frac{2 y}{3}$

$y = - 10$

$x = \frac{5}{3} + \frac{2 y}{3}$

$y = - 10$

$x = \frac{5}{3} + \frac{2 y}{3}$

Step 4

Replace all occurrences of $y$ with $- 10$ in each equation.

Replace all occurrences of $y$ in $x = \frac{5}{3} + \frac{2 y}{3}$ with $- 10$ .

$x = \frac{5}{3} + \frac{2 (- 10)}{3}$

$y = - 10$

Simplify the right side.

Simplify $\frac{5}{3} + \frac{2 (- 10)}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{5 + 2 (- 10)}{3}$

$y = - 10$

Simplify the expression.

Multiply $2$ by $- 10$ .

$x = \frac{5 - 20}{3}$

$y = - 10$

Subtract $20$ from $5$ .

$x = \frac{- 15}{3}$

$y = - 10$

Divide $- 15$ by $3$ .

$x = - 5$

$y = - 10$

$x = - 5$

$y = - 10$

$x = - 5$

$y = - 10$

$x = - 5$

$y = - 10$

$x = - 5$

$y = - 10$

Step 5

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

$(- 5, - 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, - 10)$

Equation Form:

$x = - 5, y = - 10$

Step 7

Solve by Substitution 3x-2y=5 , 4x-5y=30

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