Finite Math Examples

$x + 3 y + z = 92$ , $7 y + 2 z = 56$

Step 1

Solve the equation for $x$ .

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Step 1.1

Simplify $x + 3 (8 - \frac{2 z}{7}) + z$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$x + 3 \cdot 8 + 3 (- \frac{2 z}{7}) + z = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.1.2

Multiply $3$ by $8$ .

$x + 24 + 3 (- \frac{2 z}{7}) + z = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.1.3

Multiply $3 (- \frac{2 z}{7})$ .

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Step 1.1.1.3.1

Multiply $- 1$ by $3$ .

$x + 24 - 3 \frac{2 z}{7} + z = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.1.3.2

Combine $- 3$ and $\frac{2 z}{7}$ .

$x + 24 + \frac{- 3 (2 z)}{7} + z = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.1.3.3

Multiply $2$ by $- 3$ .

$x + 24 + \frac{- 6 z}{7} + z = 92$

$y = 8 - \frac{2 z}{7}$

$x + 24 + \frac{- 6 z}{7} + z = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.1.4

Move the negative in front of the fraction.

$x + 24 - \frac{6 z}{7} + z = 92$

$y = 8 - \frac{2 z}{7}$

$x + 24 - \frac{6 z}{7} + z = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.2

To write $z$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x + 24 - \frac{6 z}{7} + z \cdot \frac{7}{7} = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.3

Combine $z$ and $\frac{7}{7}$ .

$x + 24 - \frac{6 z}{7} + \frac{z \cdot 7}{7} = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.4

Combine the numerators over the common denominator.

$x + 24 + \frac{- 6 z + z \cdot 7}{7} = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.5

Add $- 6 z$ and $z \cdot 7$ .

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Step 1.1.5.1

Reorder $z$ and $7$ .

$x + 24 + \frac{- 6 z + 7 \cdot z}{7} = 92$

$y = 8 - \frac{2 z}{7}$

Step 1.1.5.2

Add $- 6 z$ and $7 \cdot z$ .

$x + 24 + \frac{z}{7} = 92$

$y = 8 - \frac{2 z}{7}$

$x + 24 + \frac{z}{7} = 92$

$y = 8 - \frac{2 z}{7}$

$x + 24 + \frac{z}{7} = 92$

$y = 8 - \frac{2 z}{7}$

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 $24$ from both sides of the equation.

$x + \frac{z}{7} = 92 - 24$

$y = 8 - \frac{2 z}{7}$

Step 1.2.2

Subtract $\frac{z}{7}$ from both sides of the equation.

$x = 92 - 24 - \frac{z}{7}$

$y = 8 - \frac{2 z}{7}$

Step 1.2.3

Subtract $24$ from $92$ .

$x = 68 - \frac{z}{7}$

$y = 8 - \frac{2 z}{7}$

$x = 68 - \frac{z}{7}$

$y = 8 - \frac{2 z}{7}$

$x = 68 - \frac{z}{7}$

$y = 8 - \frac{2 z}{7}$

Step 2

Simplify the right side.

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Step 2.1

Reorder $68$ and $- \frac{z}{7}$ .

$x = - \frac{z}{7} + 68$

$y = 8 - \frac{2 z}{7}$

$x = - \frac{z}{7} + 68$

$y = 8 - \frac{2 z}{7}$

Step 3

Simplify the right side.

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Step 3.1

Reorder $8$ and $- \frac{2 z}{7}$ .

$y = - \frac{2 z}{7} + 8$

$x = - \frac{z}{7} + 68$

$y = - \frac{2 z}{7} + 8$

$x = - \frac{z}{7} + 68$