Solve the System of Equations 1/2x-1/3y=5 x=2/3y+10

$\frac{1}{2} x - \frac{1}{3} y = 5$ $x = \frac{2}{3} y + 10$

Step 1

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

$x = \frac{2 y}{3} + 10$

$\frac{1}{2} x - \frac{1}{3} y = 5$

Step 2

Replace all occurrences of $x$ with $\frac{2 y}{3} + 10$ in each equation.

Replace all occurrences of $x$ in $\frac{1}{2} x - \frac{1}{3} y = 5$ with $\frac{2 y}{3} + 10$ .

$\frac{1}{2} \cdot (\frac{2 y}{3} + 10) - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Simplify the left side.

Simplify $\frac{1}{2} \cdot (\frac{2 y}{3} + 10) - \frac{1}{3} y$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} \cdot \frac{2 y}{3} + \frac{1}{2} \cdot 10 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Cancel the common factor of $2$ .

Factor $2$ out of $2 y$ .

$\frac{1}{2} \cdot \frac{2 (y)}{3} + \frac{1}{2} \cdot 10 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 y}{3} + \frac{1}{2} \cdot 10 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Rewrite the expression.

$\frac{y}{3} + \frac{1}{2} \cdot 10 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

$\frac{y}{3} + \frac{1}{2} \cdot 10 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{y}{3} + \frac{1}{2} \cdot (2 (5)) - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Cancel the common factor.

$\frac{y}{3} + \frac{1}{2} \cdot (2 \cdot 5) - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Rewrite the expression.

$\frac{y}{3} + 5 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

$\frac{y}{3} + 5 - \frac{1}{3} y = 5$

$x = \frac{2 y}{3} + 10$

Combine $y$ and $\frac{1}{3}$ .

$\frac{y}{3} + 5 - \frac{y}{3} = 5$

$x = \frac{2 y}{3} + 10$

$\frac{y}{3} + 5 - \frac{y}{3} = 5$

$x = \frac{2 y}{3} + 10$

Combine the opposite terms in $\frac{y}{3} + 5 - \frac{y}{3}$ .

Subtract $\frac{y}{3}$ from $\frac{y}{3}$ .

$0 + 5 = 5$

$x = \frac{2 y}{3} + 10$

Add $0$ and $5$ .

$5 = 5$

$x = \frac{2 y}{3} + 10$

$5 = 5$

$x = \frac{2 y}{3} + 10$

$5 = 5$

$x = \frac{2 y}{3} + 10$

$5 = 5$

$x = \frac{2 y}{3} + 10$

$5 = 5$

$x = \frac{2 y}{3} + 10$

Step 3

Remove any equations from the system that are always true.

$x = \frac{2 y}{3} + 10$

Step 4

Solve the System of Equations 1/2x-1/3y=5 x=2/3y+10

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