Finite Math Examples

$x = 3 y + 9$ , $9 - x = - 3 y$

Step 1

Replace all occurrences of $x$ with $3 y + 9$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $9 - x = - 3 y$ with $3 y + 9$ .

$9 - (3 y + 9) = - 3 y$

$x = 3 y + 9$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $9 - (3 y + 9)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$9 - (3 y) - 1 \cdot 9 = - 3 y$

$x = 3 y + 9$

Step 1.2.1.1.2

Multiply $3$ by $- 1$ .

$9 - 3 y - 1 \cdot 9 = - 3 y$

$x = 3 y + 9$

Step 1.2.1.1.3

Multiply $- 1$ by $9$ .

$9 - 3 y - 9 = - 3 y$

$x = 3 y + 9$

$9 - 3 y - 9 = - 3 y$

$x = 3 y + 9$

Step 1.2.1.2

Combine the opposite terms in $9 - 3 y - 9$ .

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Step 1.2.1.2.1

Subtract $9$ from $9$ .

$- 3 y + 0 = - 3 y$

$x = 3 y + 9$

Step 1.2.1.2.2

Add $- 3 y$ and $0$ .

$- 3 y = - 3 y$

$x = 3 y + 9$

$- 3 y = - 3 y$

$x = 3 y + 9$

$- 3 y = - 3 y$

$x = 3 y + 9$

$- 3 y = - 3 y$

$x = 3 y + 9$

$- 3 y = - 3 y$

$x = 3 y + 9$

Step 2

Remove any equations from the system that are always true.

$x = 3 y + 9$

Step 3