Finite Math Examples

$x = 5 y + 1$ , $- 3 x + 15 y = - 3$

Step 1

Replace all occurrences of $x$ with $5 y + 1$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $- 3 x + 15 y = - 3$ with $5 y + 1$ .

$- 3 (5 y + 1) + 15 y = - 3$

$x = 5 y + 1$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $- 3 (5 y + 1) + 15 y$ .

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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.

$- 3 (5 y) - 3 \cdot 1 + 15 y = - 3$

$x = 5 y + 1$

Step 1.2.1.1.2

Multiply $5$ by $- 3$ .

$- 15 y - 3 \cdot 1 + 15 y = - 3$

$x = 5 y + 1$

Step 1.2.1.1.3

Multiply $- 3$ by $1$ .

$- 15 y - 3 + 15 y = - 3$

$x = 5 y + 1$

$- 15 y - 3 + 15 y = - 3$

$x = 5 y + 1$

Step 1.2.1.2

Combine the opposite terms in $- 15 y - 3 + 15 y$ .

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Step 1.2.1.2.1

Add $- 15 y$ and $15 y$ .

$0 - 3 = - 3$

$x = 5 y + 1$

Step 1.2.1.2.2

Subtract $3$ from $0$ .

$- 3 = - 3$

$x = 5 y + 1$

$- 3 = - 3$

$x = 5 y + 1$

$- 3 = - 3$

$x = 5 y + 1$

$- 3 = - 3$

$x = 5 y + 1$

$- 3 = - 3$

$x = 5 y + 1$

Step 2

Remove any equations from the system that are always true.

$x = 5 y + 1$

Step 3