Finite Math Examples

$x + 2 y = 6$ , $4 x + 8 y = 24$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 6 - 2 y$

$4 x + 8 y = 24$

Step 2

Replace all occurrences of $x$ with $6 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $4 x + 8 y = 24$ with $6 - 2 y$ .

$4 (6 - 2 y) + 8 y = 24$

$x = 6 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (6 - 2 y) + 8 y$ .

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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.

$4 \cdot 6 + 4 (- 2 y) + 8 y = 24$

$x = 6 - 2 y$

Step 2.2.1.1.2

Multiply $4$ by $6$ .

$24 + 4 (- 2 y) + 8 y = 24$

$x = 6 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $4$ .

$24 - 8 y + 8 y = 24$

$x = 6 - 2 y$

$24 - 8 y + 8 y = 24$

$x = 6 - 2 y$

Step 2.2.1.2

Combine the opposite terms in $24 - 8 y + 8 y$ .

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Step 2.2.1.2.1

Add $- 8 y$ and $8 y$ .

$24 + 0 = 24$

$x = 6 - 2 y$

Step 2.2.1.2.2

Add $24$ and $0$ .

$24 = 24$

$x = 6 - 2 y$

$24 = 24$

$x = 6 - 2 y$

$24 = 24$

$x = 6 - 2 y$

$24 = 24$

$x = 6 - 2 y$

$24 = 24$

$x = 6 - 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 6 - 2 y$

Step 4