Finite Math Examples

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

Step 1

Divide each term in $4 y = 6 - 3 x$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 y = 6 - 3 x$ by $4$ .

$\frac{4 y}{4} = \frac{6}{4} + \frac{- 3 x}{4}$

$4 y + 4 x = 3$

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.

$\frac{4 y}{4} = \frac{6}{4} + \frac{- 3 x}{4}$

$4 y + 4 x = 3$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{4} + \frac{- 3 x}{4}$

$4 y + 4 x = 3$

$y = \frac{6}{4} + \frac{- 3 x}{4}$

$4 y + 4 x = 3$

$y = \frac{6}{4} + \frac{- 3 x}{4}$

$4 y + 4 x = 3$

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 $6$ .

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

$4 y + 4 x = 3$

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 $4$ .

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

$4 y + 4 x = 3$

Step 1.3.1.1.2.2

Cancel the common factor.

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

$4 y + 4 x = 3$

Step 1.3.1.1.2.3

Rewrite the expression.

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

$4 y + 4 x = 3$

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

$4 y + 4 x = 3$

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

$4 y + 4 x = 3$

Step 1.3.1.2

Move the negative in front of the fraction.

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

$4 y + 4 x = 3$

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

$4 y + 4 x = 3$

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

$4 y + 4 x = 3$

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

$4 y + 4 x = 3$

Step 2

Replace all occurrences of $y$ with $\frac{3}{2} - \frac{3 x}{4}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $4 y + 4 x = 3$ with $\frac{3}{2} - \frac{3 x}{4}$ .

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (\frac{3}{2} - \frac{3 x}{4}) + 4 x$ .

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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.

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Factor $2$ out of $4$ .

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

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

Step 2.2.1.1.2.2

Cancel the common factor.

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

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

Step 2.2.1.1.2.3

Rewrite the expression.

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

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

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

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

Step 2.2.1.1.3

Multiply $2$ by $3$ .

$6 + 4 (- \frac{3 x}{4}) + 4 x = 3$

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

Step 2.2.1.1.4

Cancel the common factor of $4$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$6 + 4 (\frac{- 3 x}{4}) + 4 x = 3$

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

Step 2.2.1.1.4.2

Cancel the common factor.

$6 + 4 (\frac{- 3 x}{4}) + 4 x = 3$

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

Step 2.2.1.1.4.3

Rewrite the expression.

$6 - 3 x + 4 x = 3$

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

$6 - 3 x + 4 x = 3$

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

$6 - 3 x + 4 x = 3$

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

Step 2.2.1.2

Add $- 3 x$ and $4 x$ .

$6 + x = 3$

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

$6 + x = 3$

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

$6 + x = 3$

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

$6 + x = 3$

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

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Subtract $6$ from both sides of the equation.

$x = 3 - 6$

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

Step 3.2

Subtract $6$ from $3$ .

$x = - 3$

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

$x = - 3$

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

Step 4

Replace all occurrences of $x$ with $- 3$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{3}{2} - \frac{3 x}{4}$ with $- 3$ .

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

$x = - 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{2} - \frac{3 (- 3)}{4}$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Multiply $3$ by $- 3$ .

$y = \frac{3}{2} - \frac{- 9}{4}$

$x = - 3$

Step 4.2.1.1.2

Move the negative in front of the fraction.

$y = \frac{3}{2} + \frac{9}{4}$

$x = - 3$

Step 4.2.1.1.3

Multiply $- - \frac{9}{4}$ .

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Step 4.2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$y = \frac{3}{2} + 1 (\frac{9}{4})$

$x = - 3$

Step 4.2.1.1.3.2

Multiply $\frac{9}{4}$ by $1$ .

$y = \frac{3}{2} + \frac{9}{4}$

$x = - 3$

$y = \frac{3}{2} + \frac{9}{4}$

$x = - 3$

$y = \frac{3}{2} + \frac{9}{4}$

$x = - 3$

Step 4.2.1.2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{3}{2} \cdot \frac{2}{2} + \frac{9}{4}$

$x = - 3$

Step 4.2.1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1.3.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$y = \frac{3 \cdot 2}{2 \cdot 2} + \frac{9}{4}$

$x = - 3$

Step 4.2.1.3.2

Multiply $2$ by $2$ .

$y = \frac{3 \cdot 2}{4} + \frac{9}{4}$

$x = - 3$

$y = \frac{3 \cdot 2}{4} + \frac{9}{4}$

$x = - 3$

Step 4.2.1.4

Combine the numerators over the common denominator.

$y = \frac{3 \cdot 2 + 9}{4}$

$x = - 3$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $3$ by $2$ .

$y = \frac{6 + 9}{4}$

$x = - 3$

Step 4.2.1.5.2

Add $6$ and $9$ .

$y = \frac{15}{4}$

$x = - 3$

$y = \frac{15}{4}$

$x = - 3$

$y = \frac{15}{4}$

$x = - 3$

$y = \frac{15}{4}$

$x = - 3$

$y = \frac{15}{4}$

$x = - 3$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 3, \frac{15}{4})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, \frac{15}{4})$

Equation Form:

$x = - 3, y = \frac{15}{4}$

Step 7