Finite Math Examples

$2 x - y = - 9$ , $- 4 x + 2 y = 18$

Step 1

Solve for $x$ in $2 x - y = - 9$ .

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Step 1.1

Add $y$ to both sides of the equation.

$2 x = - 9 + y$

$- 4 x + 2 y = 18$

Step 1.2

Divide each term in $2 x = - 9 + y$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = - 9 + y$ by $2$ .

$\frac{2 x}{2} = \frac{- 9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

$x = \frac{- 9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

$x = \frac{- 9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$x = - \frac{9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$- 4 x + 2 y = 18$

Step 2

Replace all occurrences of $x$ with $- \frac{9}{2} + \frac{y}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 4 x + 2 y = 18$ with $- \frac{9}{2} + \frac{y}{2}$ .

$- 4 (- \frac{9}{2} + \frac{y}{2}) + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 4 (- \frac{9}{2} + \frac{y}{2}) + 2 y$ .

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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.

$- 4 (- \frac{9}{2}) - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$- 4 (\frac{- 9}{2}) - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.2.2

Factor $2$ out of $- 4$ .

$2 (- 2) (\frac{- 9}{2}) - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.2.3

Cancel the common factor.

$2 \cdot (- 2 (\frac{- 9}{2})) - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.2.4

Rewrite the expression.

$- 2 \cdot - 9 - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$- 2 \cdot - 9 - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.3

Multiply $- 2$ by $- 9$ .

$18 - 4 \frac{y}{2} + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.4

Cancel the common factor of $2$ .

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Step 2.2.1.1.4.1

Factor $2$ out of $- 4$ .

$18 + 2 (- 2) (\frac{y}{2}) + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.4.2

Cancel the common factor.

$18 + 2 \cdot (- 2 \frac{y}{2}) + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.1.4.3

Rewrite the expression.

$18 - 2 y + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$18 - 2 y + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$18 - 2 y + 2 y = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.2

Combine the opposite terms in $18 - 2 y + 2 y$ .

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Step 2.2.1.2.1

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

$18 + 0 = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 2.2.1.2.2

Add $18$ and $0$ .

$18 = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$18 = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$18 = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$18 = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

$18 = 18$

$x = - \frac{9}{2} + \frac{y}{2}$

Step 3

Remove any equations from the system that are always true.

$x = - \frac{9}{2} + \frac{y}{2}$

Step 4