Algebra Examples

$x - 3 y = 4$ $Q x - 6 y = 8$

Step 1

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

$x = 4 + 3 y$

$Q x - 6 y = 8$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$Q \cdot 4 + Q (3 y) - 6 y = 8$

$x = 4 + 3 y$

Step 2.1.2

Move $4$ to the left of $Q$ .

$4 \cdot Q + Q (3 y) - 6 y = 8$

$x = 4 + 3 y$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$4 Q + 3 Q y - 6 y = 8$

$x = 4 + 3 y$

$4 Q + 3 Q y - 6 y = 8$

$x = 4 + 3 y$

Step 2.2

Subtract $4 Q$ from both sides of the equation.

$3 Q y - 6 y = 8 - 4 Q$

$x = 4 + 3 y$

Step 2.3

Factor $3 y$ out of $3 Q y - 6 y$ .

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Step 2.3.1

Factor $3 y$ out of $3 Q y$ .

$3 y (Q) - 6 y = 8 - 4 Q$

$x = 4 + 3 y$

Step 2.3.2

Factor $3 y$ out of $- 6 y$ .

$3 y (Q) + 3 y (- 2) = 8 - 4 Q$

$x = 4 + 3 y$

Step 2.3.3

Factor $3 y$ out of $3 y (Q) + 3 y (- 2)$ .

$3 y (Q - 2) = 8 - 4 Q$

$x = 4 + 3 y$

$3 y (Q - 2) = 8 - 4 Q$

$x = 4 + 3 y$

Step 2.4

Divide each term in $3 y (Q - 2) = 8 - 4 Q$ by $3 (Q - 2)$ and simplify.

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Step 2.4.1

Divide each term in $3 y (Q - 2) = 8 - 4 Q$ by $3 (Q - 2)$ .

$\frac{3 y (Q - 2)}{3 (Q - 2)} = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $3$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{3 y (Q - 2)}{3 (Q - 2)} = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

Step 2.4.2.1.2

Rewrite the expression.

$\frac{y (Q - 2)}{Q - 2} = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

$\frac{y (Q - 2)}{Q - 2} = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

Step 2.4.2.2

Cancel the common factor of $Q - 2$ .

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Step 2.4.2.2.1

Cancel the common factor.

$\frac{y (Q - 2)}{Q - 2} = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

Step 2.4.2.2.2

Divide $y$ by $1$ .

$y = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

$y = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

$y = \frac{8}{3 (Q - 2)} + \frac{- 4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Move the negative in front of the fraction.

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + 3 y$

Step 3

Simplify the right side.

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Step 3.1

Simplify $4 + 3 (\frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)})$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Apply the distributive property.

$x = 4 + 3 (\frac{8}{3 (Q - 2)}) + 3 (- \frac{4 Q}{3 (Q - 2)})$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Cancel the common factor.

$x = 4 + 3 (\frac{8}{3 (Q - 2)}) + 3 (- \frac{4 Q}{3 (Q - 2)})$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.2.2

Rewrite the expression.

$x = 4 + \frac{8}{Q - 2} + 3 (- \frac{4 Q}{3 (Q - 2)})$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + \frac{8}{Q - 2} + 3 (- \frac{4 Q}{3 (Q - 2)})$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.3

Cancel the common factor of $3$ .

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Step 3.1.1.3.1

Move the leading negative in $- \frac{4 Q}{3 (Q - 2)}$ into the numerator.

$x = 4 + \frac{8}{Q - 2} + 3 (\frac{- 4 Q}{3 (Q - 2)})$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.3.2

Cancel the common factor.

$x = 4 + \frac{8}{Q - 2} + 3 (\frac{- 4 Q}{3 (Q - 2)})$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.3.3

Rewrite the expression.

$x = 4 + \frac{8}{Q - 2} + \frac{- 4 Q}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + \frac{8}{Q - 2} + \frac{- 4 Q}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.4

Combine the numerators over the common denominator.

$x = 4 + \frac{8 - 4 Q}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.5

Factor $4$ out of $8 - 4 Q$ .

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Step 3.1.1.5.1

Factor $4$ out of $8$ .

$x = 4 + \frac{4 (2) - 4 Q}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.5.2

Factor $4$ out of $- 4 Q$ .

$x = 4 + \frac{4 (2) + 4 (- Q)}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.5.3

Factor $4$ out of $4 (2) + 4 (- Q)$ .

$x = 4 + \frac{4 (2 - Q)}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + \frac{4 (2 - Q)}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.6

Cancel the common factor of $2 - Q$ and $Q - 2$ .

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Step 3.1.1.6.1

Rewrite $2$ as $- 1 (- 2)$ .

$x = 4 + \frac{4 (- 1 \cdot - 2 - Q)}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.6.2

Factor $- 1$ out of $- Q$ .

$x = 4 + \frac{4 (- 1 \cdot - 2 - (Q))}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.6.3

Factor $- 1$ out of $- 1 (- 2) - (Q)$ .

$x = 4 + \frac{4 (- 1 (- 2 + Q))}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.6.4

Reorder terms.

$x = 4 + \frac{4 (- 1 (Q - 2))}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.6.5

Cancel the common factor.

$x = 4 + \frac{4 (- 1 (Q - 2))}{Q - 2}$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.6.6

Divide $4 \cdot (- 1)$ by $1$ .

$x = 4 + 4 \cdot (- 1)$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 + 4 \cdot (- 1)$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.1.7

Multiply $4$ by $- 1$ .

$x = 4 - 4$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 4 - 4$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

Step 3.1.2

Subtract $4$ from $4$ .

$x = 0$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 0$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$

$x = 0$

$y = \frac{8}{3 (Q - 2)} - \frac{4 Q}{3 (Q - 2)}$