Finite Math Examples

$y = \frac{3}{2} x - \frac{1}{2}$ , $y = - 2 x + 24$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{3}{2} x - \frac{1}{2} = - 2 x + 24$

Step 2

Solve $\frac{3}{2} x - \frac{1}{2} = - 2 x + 24$ for $x$ .

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Step 2.1

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} - \frac{1}{2} = - 2 x + 24$

Step 2.2

Move all terms containing $x$ to the left side of the equation.

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Step 2.2.1

Add $2 x$ to both sides of the equation.

$\frac{3 x}{2} - \frac{1}{2} + 2 x = 24$

Step 2.2.2

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

$\frac{3 x}{2} + 2 x \cdot \frac{2}{2} - \frac{1}{2} = 24$

Step 2.2.3

Combine $2 x$ and $\frac{2}{2}$ .

$\frac{3 x}{2} + \frac{2 x \cdot 2}{2} - \frac{1}{2} = 24$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{3 x + 2 x \cdot 2}{2} - \frac{1}{2} = 24$

Step 2.2.5

Combine the numerators over the common denominator.

$\frac{3 x + 2 x \cdot 2 - 1}{2} = 24$

Step 2.2.6

Multiply $2$ by $2$ .

$\frac{3 x + 4 x - 1}{2} = 24$

Step 2.2.7

Add $3 x$ and $4 x$ .

$\frac{7 x - 1}{2} = 24$

Step 2.3

Multiply both sides by $2$ .

$\frac{7 x - 1}{2} \cdot 2 = 24 \cdot 2$

Step 2.4

Simplify.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Cancel the common factor of $2$ .

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Step 2.4.1.1.1

Cancel the common factor.

$\frac{7 x - 1}{2} \cdot 2 = 24 \cdot 2$

Step 2.4.1.1.2

Rewrite the expression.

$7 x - 1 = 24 \cdot 2$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Multiply $24$ by $2$ .

$7 x - 1 = 48$

Step 2.5

Solve for $x$ .

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Step 2.5.1

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

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Step 2.5.1.1

Add $1$ to both sides of the equation.

$7 x = 48 + 1$

Step 2.5.1.2

Add $48$ and $1$ .

$7 x = 49$

Step 2.5.2

Divide each term in $7 x = 49$ by $7$ and simplify.

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Step 2.5.2.1

Divide each term in $7 x = 49$ by $7$ .

$\frac{7 x}{7} = \frac{49}{7}$

Step 2.5.2.2

Simplify the left side.

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Step 2.5.2.2.1

Cancel the common factor of $7$ .

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Step 2.5.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{49}{7}$

Step 2.5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{49}{7}$

Step 2.5.2.3

Simplify the right side.

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Step 2.5.2.3.1

Divide $49$ by $7$ .

$x = 7$

Step 3

Evaluate $y$ when $x = 7$ .

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Step 3.1

Substitute $7$ for $x$ .

$y = - 2 \cdot 7 + 24$

Step 3.2

Substitute $7$ for $x$ in $y = - 2 \cdot 7 + 24$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = - 2 \cdot 7 + 24$

Step 3.2.2

Simplify $- 2 \cdot 7 + 24$ .

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Step 3.2.2.1

Multiply $- 2$ by $7$ .

$y = - 14 + 24$

Step 3.2.2.2

Add $- 14$ and $24$ .

$y = 10$

Step 4

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

$(7, 10)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(7, 10)$

Equation Form:

$x = 7, y = 10$

Step 6