Finite Math Examples

$x - 2 y = - 6$ , $- x + 2 y + 6 = 0$

Step 1

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

$x = - 6 + 2 y$

$- x + 2 y + 6 = 0$

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 $- x + 2 y + 6 = 0$ with $- 6 + 2 y$ .

$- (- 6 + 2 y) + 2 y + 6 = 0$

$x = - 6 + 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$6 - (2 y) + 2 y + 6 = 0$

$x = - 6 + 2 y$

Step 2.2.1.1.2

Multiply $- 1$ by $- 6$ .

$6 - (2 y) + 2 y + 6 = 0$

$x = - 6 + 2 y$

Step 2.2.1.1.3

Multiply $2$ by $- 1$ .

$6 - 2 y + 2 y + 6 = 0$

$x = - 6 + 2 y$

$6 - 2 y + 2 y + 6 = 0$

$x = - 6 + 2 y$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Combine the opposite terms in $6 - 2 y + 2 y + 6$ .

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Step 2.2.1.2.1.1

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

$6 + 0 + 6 = 0$

$x = - 6 + 2 y$

Step 2.2.1.2.1.2

Add $6$ and $0$ .

$6 + 6 = 0$

$x = - 6 + 2 y$

$6 + 6 = 0$

$x = - 6 + 2 y$

Step 2.2.1.2.2

Add $6$ and $6$ .

$12 = 0$

$x = - 6 + 2 y$

$12 = 0$

$x = - 6 + 2 y$

$12 = 0$

$x = - 6 + 2 y$

$12 = 0$

$x = - 6 + 2 y$

$12 = 0$

$x = - 6 + 2 y$

Step 3

Since $12 = 0$ is not true, there is no solution.

No solution

Step 4