Precalculus Examples

$w - 6 z = 6$ , $x + y + 6 z = - 1$ , $0 = 0$

Step 1

Solve the equation for $x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$x + y + 6 \cdot - 1 + 6 (\frac{w}{6}) = - 1$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.1.2

Multiply $6$ by $- 1$ .

$x + y - 6 + 6 (\frac{w}{6}) = - 1$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.1.3

Cancel the common factor of $6$ .

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Step 1.1.3.1

Cancel the common factor.

$x + y - 6 + 6 (\frac{w}{6}) = - 1$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.1.3.2

Rewrite the expression.

$x + y - 6 + w = - 1$

$z = - 1 + \frac{w}{6}$

$0 = 0$

$x + y - 6 + w = - 1$

$z = - 1 + \frac{w}{6}$

$0 = 0$

$x + y - 6 + w = - 1$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.2

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

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Step 1.2.1

Subtract $y$ from both sides of the equation.

$x - 6 + w = - 1 - y$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.2.2

Add $6$ to both sides of the equation.

$x + w = - 1 - y + 6$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.2.3

Subtract $w$ from both sides of the equation.

$x = - 1 - y + 6 - w$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 1.2.4

Add $- 1$ and $6$ .

$x = - y + 5 - w$

$z = - 1 + \frac{w}{6}$

$0 = 0$

$x = - y + 5 - w$

$z = - 1 + \frac{w}{6}$

$0 = 0$

$x = - y + 5 - w$

$z = - 1 + \frac{w}{6}$

$0 = 0$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $(- y + 5 - w) + y + 6 (- 1 + \frac{w}{6})$ .

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Step 2.1.1

Combine the opposite terms in $(- y + 5 - w) + y + 6 (- 1 + \frac{w}{6})$ .

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Step 2.1.1.1

Add $- y$ and $y$ .

$5 - w + 0 + 6 (- 1 + \frac{w}{6}) = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.1.2

Add $5 - w$ and $0$ .

$5 - w + 6 (- 1 + \frac{w}{6}) = - 1$

$x = - y + 5 - w$

$0 = 0$

$5 - w + 6 (- 1 + \frac{w}{6}) = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.2

Simplify each term.

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Step 2.1.2.1

Apply the distributive property.

$5 - w + 6 \cdot - 1 + 6 (\frac{w}{6}) = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.2.2

Multiply $6$ by $- 1$ .

$5 - w - 6 + 6 (\frac{w}{6}) = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.2.3

Cancel the common factor of $6$ .

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Step 2.1.2.3.1

Cancel the common factor.

$5 - w - 6 + 6 (\frac{w}{6}) = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.2.3.2

Rewrite the expression.

$5 - w - 6 + w = - 1$

$x = - y + 5 - w$

$0 = 0$

$5 - w - 6 + w = - 1$

$x = - y + 5 - w$

$0 = 0$

$5 - w - 6 + w = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.3

Simplify by adding terms.

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Step 2.1.3.1

Combine the opposite terms in $5 - w - 6 + w$ .

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Step 2.1.3.1.1

Add $- w$ and $w$ .

$5 + 0 - 6 = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.3.1.2

Add $5$ and $0$ .

$5 - 6 = - 1$

$x = - y + 5 - w$

$0 = 0$

$5 - 6 = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.1.3.2

Subtract $6$ from $5$ .

$- 1 = - 1$

$x = - y + 5 - w$

$0 = 0$

$- 1 = - 1$

$x = - y + 5 - w$

$0 = 0$

$- 1 = - 1$

$x = - y + 5 - w$

$0 = 0$

Step 2.2

Since $- 1 = - 1$ , the equation will always be true.

Always true

$x = - y + 5 - w$

$0 = 0$

Always true

$x = - y + 5 - w$

$0 = 0$

Step 3

Simplify the right side.

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Step 3.1

Simplify $- y + 5 - w$ .

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Step 3.1.1

Move $5$ .

$x = - y - w + 5$

$0 = 0$

Step 3.1.2

Reorder $- y$ and $- w$ .

$x = - w - y + 5$

$0 = 0$

$x = - w - y + 5$

$0 = 0$

$x = - w - y + 5$

$0 = 0$

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