Finite Math Examples

$x + 2 y = 4$ , $8 x + 16 y = 32$

Step 1

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

$x = 4 - 2 y$

$8 x + 16 y = 32$

Step 2

Replace all occurrences of $x$ with $4 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $8 x + 16 y = 32$ with $4 - 2 y$ .

$8 (4 - 2 y) + 16 y = 32$

$x = 4 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $8 (4 - 2 y) + 16 y$ .

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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.

$8 \cdot 4 + 8 (- 2 y) + 16 y = 32$

$x = 4 - 2 y$

Step 2.2.1.1.2

Multiply $8$ by $4$ .

$32 + 8 (- 2 y) + 16 y = 32$

$x = 4 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $8$ .

$32 - 16 y + 16 y = 32$

$x = 4 - 2 y$

$32 - 16 y + 16 y = 32$

$x = 4 - 2 y$

Step 2.2.1.2

Combine the opposite terms in $32 - 16 y + 16 y$ .

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Step 2.2.1.2.1

Add $- 16 y$ and $16 y$ .

$32 + 0 = 32$

$x = 4 - 2 y$

Step 2.2.1.2.2

Add $32$ and $0$ .

$32 = 32$

$x = 4 - 2 y$

$32 = 32$

$x = 4 - 2 y$

$32 = 32$

$x = 4 - 2 y$

$32 = 32$

$x = 4 - 2 y$

$32 = 32$

$x = 4 - 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 - 2 y$

Step 4