Finite Math Examples

$x + 2 y = 4$ , $2 y = - x + 4$

Step 1

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

$x = 4 - 2 y$

$2 y = - x + 4$

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 $2 y = - x + 4$ with $4 - 2 y$ .

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

$x = 4 - 2 y$

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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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.

$2 y = - 1 \cdot 4 - (- 2 y) + 4$

$x = 4 - 2 y$

Step 2.2.1.1.2

Multiply $- 1$ by $4$ .

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

$x = 4 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $- 1$ .

$2 y = - 4 + 2 y + 4$

$x = 4 - 2 y$

$2 y = - 4 + 2 y + 4$

$x = 4 - 2 y$

Step 2.2.1.2

Combine the opposite terms in $- 4 + 2 y + 4$ .

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Step 2.2.1.2.1

Add $- 4$ and $4$ .

$2 y = 2 y + 0$

$x = 4 - 2 y$

Step 2.2.1.2.2

Add $2 y$ and $0$ .

$2 y = 2 y$

$x = 4 - 2 y$

$2 y = 2 y$

$x = 4 - 2 y$

$2 y = 2 y$

$x = 4 - 2 y$

$2 y = 2 y$

$x = 4 - 2 y$

$2 y = 2 y$

$x = 4 - 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 - 2 y$

Step 4