Finite Math Examples

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

Step 1

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

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Step 1.1

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

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

$2 y - 3 x = 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

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

$2 y - 3 x = 2$

Step 1.2.1.2

Divide $y$ by $1$ .

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

$2 y - 3 x = 2$

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

$2 y - 3 x = 2$

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

$2 y - 3 x = 2$

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 $6$ and $4$ .

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Step 1.3.1.1.1

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x)}{4} + \frac{4}{4}$

$2 y - 3 x = 2$

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 $4$ .

$y = \frac{2 (3 x)}{2 (2)} + \frac{4}{4}$

$2 y - 3 x = 2$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot 2} + \frac{4}{4}$

$2 y - 3 x = 2$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{3 x}{2} + \frac{4}{4}$

$2 y - 3 x = 2$

$y = \frac{3 x}{2} + \frac{4}{4}$

$2 y - 3 x = 2$

$y = \frac{3 x}{2} + \frac{4}{4}$

$2 y - 3 x = 2$

Step 1.3.1.2

Divide $4$ by $4$ .

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

$2 y - 3 x = 2$

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

$2 y - 3 x = 2$

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

$2 y - 3 x = 2$

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

$2 y - 3 x = 2$

Step 2

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

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Step 2.1

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

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

Step 2.2.1.1.2.2

Rewrite the expression.

$3 x + 2 \cdot 1 - 3 x = 2$

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

$3 x + 2 \cdot 1 - 3 x = 2$

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

Step 2.2.1.1.3

Multiply $2$ by $1$ .

$3 x + 2 - 3 x = 2$

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

$3 x + 2 - 3 x = 2$

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

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 $3 x$ .

$0 + 2 = 2$

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

Step 2.2.1.2.2

Add $0$ and $2$ .

$2 = 2$

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

$2 = 2$

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

$2 = 2$

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

$2 = 2$

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

$2 = 2$

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

Step 3

Remove any equations from the system that are always true.

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

Step 4

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