Finite Math Examples

$x - 2 y = 3$ , $8 x - 16 y = 24$ , $4 x - 8 y = 12$

Step 1

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

$x = 3 + 2 y$

$8 x - 16 y = 24$

$4 x - 8 y = 12$

Step 2

Replace all occurrences of $x$ with $3 + 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $8 x - 16 y = 24$ with $3 + 2 y$ .

$8 (3 + 2 y) - 16 y = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $8 (3 + 2 y) - 16 y$ .

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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.

$8 \cdot 3 + 8 (2 y) - 16 y = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2.2.1.1.2

Multiply $8$ by $3$ .

$24 + 8 (2 y) - 16 y = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2.2.1.1.3

Multiply $2$ by $8$ .

$24 + 16 y - 16 y = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

$24 + 16 y - 16 y = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2.2.1.2

Combine the opposite terms in $24 + 16 y - 16 y$ .

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Step 2.2.1.2.1

Subtract $16 y$ from $16 y$ .

$24 + 0 = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2.2.1.2.2

Add $24$ and $0$ .

$24 = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2.3

Replace all occurrences of $x$ in $4 x - 8 y = 12$ with $3 + 2 y$ .

$4 (3 + 2 y) - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $4 (3 + 2 y) - 8 y$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$4 \cdot 3 + 4 (2 y) - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

Step 2.4.1.1.2

Multiply $4$ by $3$ .

$12 + 4 (2 y) - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

Step 2.4.1.1.3

Multiply $2$ by $4$ .

$12 + 8 y - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

$12 + 8 y - 8 y = 12$

$24 = 24$

$x = 3 + 2 y$

Step 2.4.1.2

Combine the opposite terms in $12 + 8 y - 8 y$ .

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Step 2.4.1.2.1

Subtract $8 y$ from $8 y$ .

$12 + 0 = 12$

$24 = 24$

$x = 3 + 2 y$

Step 2.4.1.2.2

Add $12$ and $0$ .

$12 = 12$

$24 = 24$

$x = 3 + 2 y$

$12 = 12$

$24 = 24$

$x = 3 + 2 y$

$12 = 12$

$24 = 24$

$x = 3 + 2 y$

$12 = 12$

$24 = 24$

$x = 3 + 2 y$

$12 = 12$

$24 = 24$

$x = 3 + 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 3 + 2 y$

Step 4