Finite Math Examples

$x + 3 y - 9 z = 14$ , $y - 4 z = 5$

Step 1

Solve the equation for $x$ .

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Step 1.1

Simplify $x + 3 (5 + 4 z) - 9 z$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$x + 3 \cdot 5 + 3 (4 z) - 9 z = 14$

$y = 5 + 4 z$

Step 1.1.1.2

Multiply $3$ by $5$ .

$x + 15 + 3 (4 z) - 9 z = 14$

$y = 5 + 4 z$

Step 1.1.1.3

Multiply $4$ by $3$ .

$x + 15 + 12 z - 9 z = 14$

$y = 5 + 4 z$

$x + 15 + 12 z - 9 z = 14$

$y = 5 + 4 z$

Step 1.1.2

Subtract $9 z$ from $12 z$ .

$x + 15 + 3 z = 14$

$y = 5 + 4 z$

$x + 15 + 3 z = 14$

$y = 5 + 4 z$

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 $15$ from both sides of the equation.

$x + 3 z = 14 - 15$

$y = 5 + 4 z$

Step 1.2.2

Subtract $3 z$ from both sides of the equation.

$x = 14 - 15 - 3 z$

$y = 5 + 4 z$

Step 1.2.3

Subtract $15$ from $14$ .

$x = - 1 - 3 z$

$y = 5 + 4 z$

$x = - 1 - 3 z$

$y = 5 + 4 z$

$x = - 1 - 3 z$

$y = 5 + 4 z$

Step 2

Simplify the right side.

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Step 2.1

Reorder $- 1$ and $- 3 z$ .

$x = - 3 z - 1$

$y = 5 + 4 z$

$x = - 3 z - 1$

$y = 5 + 4 z$

Step 3

Simplify the right side.

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Step 3.1

Reorder $5$ and $4 z$ .

$y = 4 z + 5$

$x = - 3 z - 1$

$y = 4 z + 5$

$x = - 3 z - 1$

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