Finite Math Examples

$\frac{3}{2} x - \frac{2}{3} y = \frac{23}{2}$ , $\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1

Solve for $x$ in $\frac{3}{2} x - \frac{2}{3} y = \frac{23}{2}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

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

$\frac{3 x}{2} - \frac{2}{3} y = \frac{23}{2}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.1.2

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

$\frac{3 x}{2} - \frac{y \cdot 2}{3} = \frac{23}{2}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.1.3

Move $2$ to the left of $y$ .

$\frac{3 x}{2} - \frac{2 y}{3} = \frac{23}{2}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$\frac{3 x}{2} - \frac{2 y}{3} = \frac{23}{2}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.2

Add $\frac{2 y}{3}$ to both sides of the equation.

$\frac{3 x}{2} = \frac{23}{2} + \frac{2 y}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.3

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4

Simplify both sides of the equation.

Tap for more steps...

Step 1.4.1

Simplify the left side.

Tap for more steps...

Step 1.4.1.1

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Tap for more steps...

Step 1.4.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.4.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} \cdot (3 x) = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$\frac{1}{3} \cdot (3 x) = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.4.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} \cdot (3 (x)) = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 x) = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{2}{3} \cdot (\frac{23}{2} + \frac{2 y}{3})$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2

Simplify the right side.

Tap for more steps...

Step 1.4.2.1

Simplify $\frac{2}{3} (\frac{23}{2} + \frac{2 y}{3})$ .

Tap for more steps...

Step 1.4.2.1.1

Apply the distributive property.

$x = \frac{2}{3} \cdot \frac{23}{2} + \frac{2}{3} \cdot \frac{2 y}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.4.2.1.2.1

Cancel the common factor.

$x = \frac{2}{3} \cdot \frac{23}{2} + \frac{2}{3} \cdot \frac{2 y}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2.1.2.2

Rewrite the expression.

$x = \frac{1}{3} \cdot 23 + \frac{2}{3} \cdot \frac{2 y}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{1}{3} \cdot 23 + \frac{2}{3} \cdot \frac{2 y}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2.1.3

Combine $\frac{1}{3}$ and $23$ .

$x = \frac{23}{3} + \frac{2}{3} \cdot \frac{2 y}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2.1.4

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

Tap for more steps...

Step 1.4.2.1.4.1

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

$x = \frac{23}{3} + \frac{2 (2 y)}{3 \cdot 3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2.1.4.2

Multiply $2$ by $2$ .

$x = \frac{23}{3} + \frac{4 y}{3 \cdot 3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.4.2.1.4.3

Multiply $3$ by $3$ .

$x = \frac{23}{3} + \frac{4 y}{9}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{23}{3} + \frac{4 y}{9}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{23}{3} + \frac{4 y}{9}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{23}{3} + \frac{4 y}{9}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{23}{3} + \frac{4 y}{9}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 1.5

Reorder $\frac{23}{3}$ and $\frac{4 y}{9}$ .

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$

Step 2

Replace all occurrences of $x$ with $\frac{4 y}{9} + \frac{23}{3}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $\frac{2}{5} x - \frac{1}{3} y = \frac{13}{5}$ with $\frac{4 y}{9} + \frac{23}{3}$ .

$\frac{2}{5} \cdot (\frac{4 y}{9} + \frac{23}{3}) - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $\frac{2}{5} \cdot (\frac{4 y}{9} + \frac{23}{3}) - \frac{1}{3} y$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$\frac{2}{5} \cdot \frac{4 y}{9} + \frac{2}{5} \cdot \frac{23}{3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.2

Multiply $\frac{2}{5} \cdot \frac{4 y}{9}$ .

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $\frac{2}{5}$ by $\frac{4 y}{9}$ .

$\frac{2 (4 y)}{5 \cdot 9} + \frac{2}{5} \cdot \frac{23}{3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.2.2

Multiply $4$ by $2$ .

$\frac{8 y}{5 \cdot 9} + \frac{2}{5} \cdot \frac{23}{3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.2.3

Multiply $5$ by $9$ .

$\frac{8 y}{45} + \frac{2}{5} \cdot \frac{23}{3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{8 y}{45} + \frac{2}{5} \cdot \frac{23}{3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.3

Multiply $\frac{2}{5} \cdot \frac{23}{3}$ .

Tap for more steps...

Step 2.2.1.1.3.1

Multiply $\frac{2}{5}$ by $\frac{23}{3}$ .

$\frac{8 y}{45} + \frac{2 \cdot 23}{5 \cdot 3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.3.2

Multiply $2$ by $23$ .

$\frac{8 y}{45} + \frac{46}{5 \cdot 3} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.3.3

Multiply $5$ by $3$ .

$\frac{8 y}{45} + \frac{46}{15} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{8 y}{45} + \frac{46}{15} - \frac{1}{3} y = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.1.4

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

$\frac{8 y}{45} + \frac{46}{15} - \frac{y}{3} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{8 y}{45} + \frac{46}{15} - \frac{y}{3} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.2

To write $- \frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{8 y}{45} - \frac{y}{3} \cdot \frac{15}{15} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.3

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.2.1.3.1

Multiply $\frac{y}{3}$ by $\frac{15}{15}$ .

$\frac{8 y}{45} - \frac{y \cdot 15}{3 \cdot 15} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.3.2

Multiply $3$ by $15$ .

$\frac{8 y}{45} - \frac{y \cdot 15}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{8 y}{45} - \frac{y \cdot 15}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{8 y - y \cdot 15}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5

Simplify each term.

Tap for more steps...

Step 2.2.1.5.1

Simplify the numerator.

Tap for more steps...

Step 2.2.1.5.1.1

Factor $y$ out of $8 y - y \cdot 15$ .

Tap for more steps...

Step 2.2.1.5.1.1.1

Factor $y$ out of $8 y$ .

$\frac{y \cdot 8 - y \cdot 15}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5.1.1.2

Factor $y$ out of $- y \cdot 15$ .

$\frac{y \cdot 8 + y (- 1 \cdot 15)}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5.1.1.3

Factor $y$ out of $y \cdot 8 + y (- 1 \cdot 15)$ .

$\frac{y (8 - 1 \cdot 15)}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{y (8 - 1 \cdot 15)}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5.1.2

Multiply $- 1$ by $15$ .

$\frac{y (8 - 15)}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5.1.3

Subtract $15$ from $8$ .

$\frac{y \cdot - 7}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{y \cdot - 7}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5.2

Move $- 7$ to the left of $y$ .

$\frac{- 7 \cdot y}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 2.2.1.5.3

Move the negative in front of the fraction.

$- \frac{7 y}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} + \frac{46}{15} = \frac{13}{5}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3

Solve for $y$ in $- \frac{7 y}{45} + \frac{46}{15} = \frac{13}{5}$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $\frac{46}{15}$ from both sides of the equation.

$- \frac{7 y}{45} = \frac{13}{5} - \frac{46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.2

To write $\frac{13}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7 y}{45} = \frac{13}{5} \cdot \frac{3}{3} - \frac{46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1.3.1

Multiply $\frac{13}{5}$ by $\frac{3}{3}$ .

$- \frac{7 y}{45} = \frac{13 \cdot 3}{5 \cdot 3} - \frac{46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.3.2

Multiply $5$ by $3$ .

$- \frac{7 y}{45} = \frac{13 \cdot 3}{15} - \frac{46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} = \frac{13 \cdot 3}{15} - \frac{46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.4

Combine the numerators over the common denominator.

$- \frac{7 y}{45} = \frac{13 \cdot 3 - 46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.5

Simplify the numerator.

Tap for more steps...

Step 3.1.5.1

Multiply $13$ by $3$ .

$- \frac{7 y}{45} = \frac{39 - 46}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.5.2

Subtract $46$ from $39$ .

$- \frac{7 y}{45} = \frac{- 7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} = \frac{- 7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.1.6

Move the negative in front of the fraction.

$- \frac{7 y}{45} = - \frac{7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

$- \frac{7 y}{45} = - \frac{7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.2

Multiply both sides of the equation by $- \frac{45}{7}$ .

$- \frac{45}{7} \cdot (- \frac{7 y}{45}) = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3

Simplify both sides of the equation.

Tap for more steps...

Step 3.3.1

Simplify the left side.

Tap for more steps...

Step 3.3.1.1

Simplify $- \frac{45}{7} (- \frac{7 y}{45})$ .

Tap for more steps...

Step 3.3.1.1.1

Cancel the common factor of $45$ .

Tap for more steps...

Step 3.3.1.1.1.1

Move the leading negative in $- \frac{45}{7}$ into the numerator.

$\frac{- 45}{7} \cdot (- \frac{7 y}{45}) = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.1.2

Move the leading negative in $- \frac{7 y}{45}$ into the numerator.

$\frac{- 45}{7} \cdot \frac{- 7 y}{45} = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.1.3

Factor $45$ out of $- 45$ .

$\frac{45 (- 1)}{7} \cdot \frac{- 7 y}{45} = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.1.4

Cancel the common factor.

$\frac{45 \cdot - 1}{7} \cdot \frac{- 7 y}{45} = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} \cdot (- 7 y) = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

$\frac{- 1}{7} \cdot (- 7 y) = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.2

Cancel the common factor of $7$ .

Tap for more steps...

Step 3.3.1.1.2.1

Factor $7$ out of $- 7 y$ .

$\frac{- 1}{7} \cdot (7 (- y)) = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} \cdot (7 (- y)) = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.3

Multiply.

Tap for more steps...

Step 3.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = - \frac{45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.1

Simplify $- \frac{45}{7} (- \frac{7}{15})$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.3.2.1.1.1

Move the leading negative in $- \frac{45}{7}$ into the numerator.

$y = \frac{- 45}{7} \cdot (- \frac{7}{15})$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.1.2

Move the leading negative in $- \frac{7}{15}$ into the numerator.

$y = \frac{- 45}{7} \cdot \frac{- 7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.1.3

Factor $15$ out of $- 45$ .

$y = \frac{15 (- 3)}{7} \cdot \frac{- 7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.1.4

Cancel the common factor.

$y = \frac{15 \cdot - 3}{7} \cdot \frac{- 7}{15}$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.1.5

Rewrite the expression.

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

$x = \frac{4 y}{9} + \frac{23}{3}$

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

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.2

Cancel the common factor of $7$ .

Tap for more steps...

Step 3.3.2.1.2.1

Factor $7$ out of $- 7$ .

$y = \frac{- 3}{7} \cdot (7 (- 1))$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.2.2

Cancel the common factor.

$y = \frac{- 3}{7} \cdot (7 \cdot - 1)$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.2.3

Rewrite the expression.

$y = - 3 \cdot - 1$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = - 3 \cdot - 1$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 3.3.2.1.3

Multiply $- 3$ by $- 1$ .

$y = 3$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = 3$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = 3$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = 3$

$x = \frac{4 y}{9} + \frac{23}{3}$

$y = 3$

$x = \frac{4 y}{9} + \frac{23}{3}$

Step 4

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

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = \frac{4 y}{9} + \frac{23}{3}$ with $3$ .

$x = \frac{4 (3)}{9} + \frac{23}{3}$

$y = 3$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{4 (3)}{9} + \frac{23}{3}$ .

Tap for more steps...

Step 4.2.1.1

Multiply $4$ by $3$ .

$x = \frac{12}{9} + \frac{23}{3}$

$y = 3$

Step 4.2.1.2

Cancel the common factor of $12$ and $9$ .

Tap for more steps...

Step 4.2.1.2.1

Factor $3$ out of $12$ .

$x = \frac{3 (4)}{9} + \frac{23}{3}$

$y = 3$

Step 4.2.1.2.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1.2.2.1

Factor $3$ out of $9$ .

$x = \frac{3 \cdot 4}{3 \cdot 3} + \frac{23}{3}$

$y = 3$

Step 4.2.1.2.2.2

Cancel the common factor.

$x = \frac{3 \cdot 4}{3 \cdot 3} + \frac{23}{3}$

$y = 3$

Step 4.2.1.2.2.3

Rewrite the expression.

$x = \frac{4}{3} + \frac{23}{3}$

$y = 3$

$x = \frac{4}{3} + \frac{23}{3}$

$y = 3$

$x = \frac{4}{3} + \frac{23}{3}$

$y = 3$

Step 4.2.1.3

Combine the numerators over the common denominator.

$x = \frac{4 + 23}{3}$

$y = 3$

Step 4.2.1.4

Simplify the expression.

Tap for more steps...

Step 4.2.1.4.1

Add $4$ and $23$ .

$x = \frac{27}{3}$

$y = 3$

Step 4.2.1.4.2

Divide $27$ by $3$ .

$x = 9$

$y = 3$

$x = 9$

$y = 3$

$x = 9$

$y = 3$

$x = 9$

$y = 3$

$x = 9$

$y = 3$

Step 5

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

$(9, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 3)$

Equation Form:

$x = 9, y = 3$

Step 7