Precalculus Examples

$x - y + z = 7$ , $4 x + 3 y - 3 z = 0$

Step 1

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

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Step 1.1

Add $y$ to both sides of the equation.

$x + z = 7 + y$

$4 x + 3 y - 3 z = 0$

Step 1.2

Subtract $z$ from both sides of the equation.

$x = 7 + y - z$

$4 x + 3 y - 3 z = 0$

$x = 7 + y - z$

$4 x + 3 y - 3 z = 0$

Step 2

Solve the equation for $z$ .

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Step 2.1

Simplify $4 (7 + y - z) + 3 y - 3 z$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$4 \cdot 7 + 4 y + 4 (- z) + 3 y - 3 z = 0$

$x = 7 + y - z$

Step 2.1.1.2

Simplify.

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Step 2.1.1.2.1

Multiply $4$ by $7$ .

$28 + 4 y + 4 (- z) + 3 y - 3 z = 0$

$x = 7 + y - z$

Step 2.1.1.2.2

Multiply $- 1$ by $4$ .

$28 + 4 y - 4 z + 3 y - 3 z = 0$

$x = 7 + y - z$

$28 + 4 y - 4 z + 3 y - 3 z = 0$

$x = 7 + y - z$

$28 + 4 y - 4 z + 3 y - 3 z = 0$

$x = 7 + y - z$

Step 2.1.2

Simplify by adding terms.

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Step 2.1.2.1

Add $4 y$ and $3 y$ .

$28 + 7 y - 4 z - 3 z = 0$

$x = 7 + y - z$

Step 2.1.2.2

Subtract $3 z$ from $- 4 z$ .

$28 + 7 y - 7 z = 0$

$x = 7 + y - z$

$28 + 7 y - 7 z = 0$

$x = 7 + y - z$

$28 + 7 y - 7 z = 0$

$x = 7 + y - z$

Step 2.2

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

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Step 2.2.1

Subtract $28$ from both sides of the equation.

$7 y - 7 z = - 28$

$x = 7 + y - z$

Step 2.2.2

Subtract $7 y$ from both sides of the equation.

$- 7 z = - 28 - 7 y$

$x = 7 + y - z$

$- 7 z = - 28 - 7 y$

$x = 7 + y - z$

Step 2.3

Divide each term in $- 7 z = - 28 - 7 y$ by $- 7$ and simplify.

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Step 2.3.1

Divide each term in $- 7 z = - 28 - 7 y$ by $- 7$ .

$\frac{- 7 z}{- 7} = \frac{- 28}{- 7} + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 7 z}{- 7} = \frac{- 28}{- 7} + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

Step 2.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 28}{- 7} + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

$z = \frac{- 28}{- 7} + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

$z = \frac{- 28}{- 7} + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Divide $- 28$ by $- 7$ .

$z = 4 + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

Step 2.3.3.1.2

Cancel the common factor of $- 7$ .

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Step 2.3.3.1.2.1

Cancel the common factor.

$z = 4 + \frac{- 7 y}{- 7}$

$x = 7 + y - z$

Step 2.3.3.1.2.2

Divide $y$ by $1$ .

$z = 4 + y$

$x = 7 + y - z$

$z = 4 + y$

$x = 7 + y - z$

$z = 4 + y$

$x = 7 + y - z$

$z = 4 + y$

$x = 7 + y - z$

$z = 4 + y$

$x = 7 + y - z$

$z = 4 + y$

$x = 7 + y - z$

Step 3

Simplify the right side.

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Step 3.1

Simplify $7 + y - (4 + y)$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Apply the distributive property.

$x = 7 + y - 1 \cdot 4 - y$

$z = 4 + y$

Step 3.1.1.2

Multiply $- 1$ by $4$ .

$x = 7 + y - 4 - y$

$z = 4 + y$

$x = 7 + y - 4 - y$

$z = 4 + y$

Step 3.1.2

Simplify by adding terms.

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Step 3.1.2.1

Combine the opposite terms in $7 + y - 4 - y$ .

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Step 3.1.2.1.1

Subtract $y$ from $y$ .

$x = 7 + 0 - 4$

$z = 4 + y$

Step 3.1.2.1.2

Add $7$ and $0$ .

$x = 7 - 4$

$z = 4 + y$

$x = 7 - 4$

$z = 4 + y$

Step 3.1.2.2

Subtract $4$ from $7$ .

$x = 3$

$z = 4 + y$

$x = 3$

$z = 4 + y$

$x = 3$

$z = 4 + y$

$x = 3$

$z = 4 + y$

Step 4

Simplify the right side.

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Step 4.1

Reorder $4$ and $y$ .

$z = y + 4$

$x = 3$

$z = y + 4$

$x = 3$