Finite Math Examples

$3 y - 3 x = 2$ , $6 y = 6 x + 4$

Step 1

Divide each term in $6 y = 6 x + 4$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 y = 6 x + 4$ by $6$ .

$\frac{6 y}{6} = \frac{6 x}{6} + \frac{4}{6}$

$3 y - 3 x = 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{6 x}{6} + \frac{4}{6}$

$3 y - 3 x = 2$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{6} + \frac{4}{6}$

$3 y - 3 x = 2$

$y = \frac{6 x}{6} + \frac{4}{6}$

$3 y - 3 x = 2$

$y = \frac{6 x}{6} + \frac{4}{6}$

$3 y - 3 x = 2$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $6$ .

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Step 1.3.1.1.1

Cancel the common factor.

$y = \frac{6 x}{6} + \frac{4}{6}$

$3 y - 3 x = 2$

Step 1.3.1.1.2

Divide $x$ by $1$ .

$y = x + \frac{4}{6}$

$3 y - 3 x = 2$

$y = x + \frac{4}{6}$

$3 y - 3 x = 2$

Step 1.3.1.2

Cancel the common factor of $4$ and $6$ .

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Step 1.3.1.2.1

Factor $2$ out of $4$ .

$y = x + \frac{2 (2)}{6}$

$3 y - 3 x = 2$

Step 1.3.1.2.2

Cancel the common factors.

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Step 1.3.1.2.2.1

Factor $2$ out of $6$ .

$y = x + \frac{2 \cdot 2}{2 \cdot 3}$

$3 y - 3 x = 2$

Step 1.3.1.2.2.2

Cancel the common factor.

$y = x + \frac{2 \cdot 2}{2 \cdot 3}$

$3 y - 3 x = 2$

Step 1.3.1.2.2.3

Rewrite the expression.

$y = x + \frac{2}{3}$

$3 y - 3 x = 2$

$y = x + \frac{2}{3}$

$3 y - 3 x = 2$

$y = x + \frac{2}{3}$

$3 y - 3 x = 2$

$y = x + \frac{2}{3}$

$3 y - 3 x = 2$

$y = x + \frac{2}{3}$

$3 y - 3 x = 2$

$y = x + \frac{2}{3}$

$3 y - 3 x = 2$

Step 2

Replace all occurrences of $y$ with $x + \frac{2}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 y - 3 x = 2$ with $x + \frac{2}{3}$ .

$3 (x + \frac{2}{3}) - 3 x = 2$

$y = x + \frac{2}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (x + \frac{2}{3}) - 3 x$ .

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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.

$3 x + 3 (\frac{2}{3}) - 3 x = 2$

$y = x + \frac{2}{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

$3 x + 3 (\frac{2}{3}) - 3 x = 2$

$y = x + \frac{2}{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

$3 x + 2 - 3 x = 2$

$y = x + \frac{2}{3}$

$3 x + 2 - 3 x = 2$

$y = x + \frac{2}{3}$

$3 x + 2 - 3 x = 2$

$y = x + \frac{2}{3}$

Step 2.2.1.2

Combine the opposite terms in $3 x + 2 - 3 x$ .

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Step 2.2.1.2.1

Subtract $3 x$ from $3 x$ .

$0 + 2 = 2$

$y = x + \frac{2}{3}$

Step 2.2.1.2.2

Add $0$ and $2$ .

$2 = 2$

$y = x + \frac{2}{3}$

$2 = 2$

$y = x + \frac{2}{3}$

$2 = 2$

$y = x + \frac{2}{3}$

$2 = 2$

$y = x + \frac{2}{3}$

$2 = 2$

$y = x + \frac{2}{3}$

Step 3

Remove any equations from the system that are always true.

$y = x + \frac{2}{3}$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$