Finite Math Examples

$x = 9 y + 3$ , $3 x - 27 y = 9$

Step 1

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

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Step 1.1

Replace all occurrences of $x$ in $3 x - 27 y = 9$ with $9 y + 3$ .

$3 (9 y + 3) - 27 y = 9$

$x = 9 y + 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $3 (9 y + 3) - 27 y$ .

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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.

$3 (9 y) + 3 \cdot 3 - 27 y = 9$

$x = 9 y + 3$

Step 1.2.1.1.2

Multiply $9$ by $3$ .

$27 y + 3 \cdot 3 - 27 y = 9$

$x = 9 y + 3$

Step 1.2.1.1.3

Multiply $3$ by $3$ .

$27 y + 9 - 27 y = 9$

$x = 9 y + 3$

$27 y + 9 - 27 y = 9$

$x = 9 y + 3$

Step 1.2.1.2

Combine the opposite terms in $27 y + 9 - 27 y$ .

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Step 1.2.1.2.1

Subtract $27 y$ from $27 y$ .

$0 + 9 = 9$

$x = 9 y + 3$

Step 1.2.1.2.2

Add $0$ and $9$ .

$9 = 9$

$x = 9 y + 3$

$9 = 9$

$x = 9 y + 3$

$9 = 9$

$x = 9 y + 3$

$9 = 9$

$x = 9 y + 3$

$9 = 9$

$x = 9 y + 3$

Step 2

Remove any equations from the system that are always true.

$x = 9 y + 3$

Step 3