Finite Math Examples

$6 x - 6 y + z = 15$ , $x + y = 5$

Step 1

Solve the equation for $z$ .

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Step 1.1

Simplify $6 (5 - y) - 6 y + z$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$6 \cdot 5 + 6 (- y) - 6 y + z = 15$

$x = 5 - y$

Step 1.1.1.2

Multiply $6$ by $5$ .

$30 + 6 (- y) - 6 y + z = 15$

$x = 5 - y$

Step 1.1.1.3

Multiply $- 1$ by $6$ .

$30 - 6 y - 6 y + z = 15$

$x = 5 - y$

$30 - 6 y - 6 y + z = 15$

$x = 5 - y$

Step 1.1.2

Subtract $6 y$ from $- 6 y$ .

$30 - 12 y + z = 15$

$x = 5 - y$

$30 - 12 y + z = 15$

$x = 5 - y$

Step 1.2

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

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Step 1.2.1

Subtract $30$ from both sides of the equation.

$- 12 y + z = 15 - 30$

$x = 5 - y$

Step 1.2.2

Add $12 y$ to both sides of the equation.

$z = 15 - 30 + 12 y$

$x = 5 - y$

Step 1.2.3

Subtract $30$ from $15$ .

$z = - 15 + 12 y$

$x = 5 - y$

$z = - 15 + 12 y$

$x = 5 - y$

$z = - 15 + 12 y$

$x = 5 - y$

Step 2

Simplify the right side.

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Step 2.1

Reorder $- 15$ and $12 y$ .

$z = 12 y - 15$

$x = 5 - y$

$z = 12 y - 15$

$x = 5 - y$

Step 3

Simplify the right side.

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Step 3.1

Reorder $5$ and $- y$ .

$x = - y + 5$

$z = 12 y - 15$

$x = - y + 5$

$z = 12 y - 15$

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