Finite Math Examples

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

Step 1

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

$x = 2 + 2 y$

$- x + 2 y = 2$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $- x + 2 y = 2$ with $2 + 2 y$ .

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

$x = 2 + 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

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

$x = 2 + 2 y$

Step 2.2.1.1.2

Multiply $- 1$ by $2$ .

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

$x = 2 + 2 y$

Step 2.2.1.1.3

Multiply $2$ by $- 1$ .

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

$x = 2 + 2 y$

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

$x = 2 + 2 y$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Add $- 2 y$ and $2 y$ .

$- 2 + 0 = 2$

$x = 2 + 2 y$

Step 2.2.1.2.2

Add $- 2$ and $0$ .

$- 2 = 2$

$x = 2 + 2 y$

$- 2 = 2$

$x = 2 + 2 y$

$- 2 = 2$

$x = 2 + 2 y$

$- 2 = 2$

$x = 2 + 2 y$

$- 2 = 2$

$x = 2 + 2 y$

Step 3

Since $- 2 = 2$ is not true, there is no solution.

No solution

Step 4