Finite Math Examples

$x - 2 y = - 5$ , $3 x - 6 y = - 15$

Step 1

Add $2 y$ to both sides of the equation.

$x = - 5 + 2 y$

$3 x - 6 y = - 15$

Step 2

Replace all occurrences of $x$ with $- 5 + 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x - 6 y = - 15$ with $- 5 + 2 y$ .

$3 (- 5 + 2 y) - 6 y = - 15$

$x = - 5 + 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (- 5 + 2 y) - 6 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$3 \cdot - 5 + 3 (2 y) - 6 y = - 15$

$x = - 5 + 2 y$

Step 2.2.1.1.2

Multiply $3$ by $- 5$ .

$- 15 + 3 (2 y) - 6 y = - 15$

$x = - 5 + 2 y$

Step 2.2.1.1.3

Multiply $2$ by $3$ .

$- 15 + 6 y - 6 y = - 15$

$x = - 5 + 2 y$

$- 15 + 6 y - 6 y = - 15$

$x = - 5 + 2 y$

Step 2.2.1.2

Combine the opposite terms in $- 15 + 6 y - 6 y$ .

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Step 2.2.1.2.1

Subtract $6 y$ from $6 y$ .

$- 15 + 0 = - 15$

$x = - 5 + 2 y$

Step 2.2.1.2.2

Add $- 15$ and $0$ .

$- 15 = - 15$

$x = - 5 + 2 y$

$- 15 = - 15$

$x = - 5 + 2 y$

$- 15 = - 15$

$x = - 5 + 2 y$

$- 15 = - 15$

$x = - 5 + 2 y$

$- 15 = - 15$

$x = - 5 + 2 y$

Step 3

Remove any equations from the system that are always true.

$x = - 5 + 2 y$

Step 4