Precalculus Examples

$x - 3 y = 4$ , $2 x + Q y = 8$

Step 1

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

$x = 4 + 3 y$

$2 x + Q y = 8$

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.

$2 \cdot 4 + 2 (3 y) + Q y = 8$

$x = 4 + 3 y$

Step 2.1.2

Multiply $2$ by $4$ .

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

$x = 4 + 3 y$

Step 2.1.3

Multiply $3$ by $2$ .

$8 + 6 y + Q y = 8$

$x = 4 + 3 y$

$8 + 6 y + Q y = 8$

$x = 4 + 3 y$

Step 2.2

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

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Step 2.2.1

Subtract $8$ from both sides of the equation.

$6 y + Q y = 8 - 8$

$x = 4 + 3 y$

Step 2.2.2

Subtract $8$ from $8$ .

$6 y + Q y = 0$

$x = 4 + 3 y$

$6 y + Q y = 0$

$x = 4 + 3 y$

Step 2.3

Factor $y$ out of $6 y + Q y$ .

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Step 2.3.1

Factor $y$ out of $6 y$ .

$y \cdot 6 + Q y = 0$

$x = 4 + 3 y$

Step 2.3.2

Factor $y$ out of $Q y$ .

$y \cdot 6 + y Q = 0$

$x = 4 + 3 y$

Step 2.3.3

Factor $y$ out of $y \cdot 6 + y Q$ .

$y \cdot (6 + Q) = 0$

$x = 4 + 3 y$

Step 2.3.4

Multiply $y$ by $6 + Q$ .

$y (6 + Q) = 0$

$x = 4 + 3 y$

$y (6 + Q) = 0$

$x = 4 + 3 y$

Step 2.4

Divide each term in $y (6 + Q) = 0$ by $6 + Q$ and simplify.

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Step 2.4.1

Divide each term in $y (6 + Q) = 0$ by $6 + Q$ .

$\frac{y (6 + Q)}{6 + Q} = \frac{0}{6 + Q}$

$x = 4 + 3 y$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $6 + Q$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{y (6 + Q)}{6 + Q} = \frac{0}{6 + Q}$

$x = 4 + 3 y$

Step 2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{6 + Q}$

$x = 4 + 3 y$

$y = \frac{0}{6 + Q}$

$x = 4 + 3 y$

$y = \frac{0}{6 + Q}$

$x = 4 + 3 y$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $0$ by $6 + Q$ .

$y = 0$

$x = 4 + 3 y$

$y = 0$

$x = 4 + 3 y$

$y = 0$

$x = 4 + 3 y$

$y = 0$

$x = 4 + 3 y$

Step 3

Simplify the right side.

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Step 3.1

Simplify $4 + 3 (0)$ .

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Step 3.1.1

Multiply $3$ by $0$ .

$x = 4 + 0$

$y = 0$

Step 3.1.2

Add $4$ and $0$ .

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$