Finite Math Examples

$3 y - 2 x = 1$ , $6 y = 4 x + 2$

Step 1

Divide each term in $6 y = 4 x + 2$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 y = 4 x + 2$ by $6$ .

$\frac{6 y}{6} = \frac{4 x}{6} + \frac{2}{6}$

$3 y - 2 x = 1$

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.

$\frac{6 y}{6} = \frac{4 x}{6} + \frac{2}{6}$

$3 y - 2 x = 1$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{6} + \frac{2}{6}$

$3 y - 2 x = 1$

$y = \frac{4 x}{6} + \frac{2}{6}$

$3 y - 2 x = 1$

$y = \frac{4 x}{6} + \frac{2}{6}$

$3 y - 2 x = 1$

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 $4$ and $6$ .

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Step 1.3.1.1.1

Factor $2$ out of $4 x$ .

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

$3 y - 2 x = 1$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $6$ .

$y = \frac{2 (2 x)}{2 (3)} + \frac{2}{6}$

$3 y - 2 x = 1$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (2 x)}{2 \cdot 3} + \frac{2}{6}$

$3 y - 2 x = 1$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{2 x}{3} + \frac{2}{6}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{2}{6}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{2}{6}$

$3 y - 2 x = 1$

Step 1.3.1.2

Cancel the common factor of $2$ and $6$ .

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Step 1.3.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 x}{3} + \frac{2 (1)}{6}$

$3 y - 2 x = 1$

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 $6$ .

$y = \frac{2 x}{3} + \frac{2 \cdot 1}{2 \cdot 3}$

$3 y - 2 x = 1$

Step 1.3.1.2.2.2

Cancel the common factor.

$y = \frac{2 x}{3} + \frac{2 \cdot 1}{2 \cdot 3}$

$3 y - 2 x = 1$

Step 1.3.1.2.2.3

Rewrite the expression.

$y = \frac{2 x}{3} + \frac{1}{3}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$3 y - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$3 y - 2 x = 1$

Step 2

Replace all occurrences of $y$ with $\frac{2 x}{3} + \frac{1}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 y - 2 x = 1$ with $\frac{2 x}{3} + \frac{1}{3}$ .

$3 (\frac{2 x}{3} + \frac{1}{3}) - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (\frac{2 x}{3} + \frac{1}{3}) - 2 x$ .

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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.

$3 (\frac{2 x}{3}) + 3 (\frac{1}{3}) - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

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.

$3 (\frac{2 x}{3}) + 3 (\frac{1}{3}) - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

$2 x + 3 (\frac{1}{3}) - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$2 x + 3 (\frac{1}{3}) - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 2.2.1.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.1.3.1

Cancel the common factor.

$2 x + 3 (\frac{1}{3}) - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 2.2.1.1.3.2

Rewrite the expression.

$2 x + 1 - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$2 x + 1 - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$2 x + 1 - 2 x = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 2.2.1.2

Combine the opposite terms in $2 x + 1 - 2 x$ .

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Step 2.2.1.2.1

Subtract $2 x$ from $2 x$ .

$0 + 1 = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 2.2.1.2.2

Add $0$ and $1$ .

$1 = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$1 = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$1 = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$1 = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

$1 = 1$

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 3

Remove any equations from the system that are always true.

$y = \frac{2 x}{3} + \frac{1}{3}$

Step 4