Finite Math Examples

$y = 10 x - 2$ , $y = 3 x + 9$

Step 1

Eliminate the equal sides of each equation and combine.

$10 x - 2 = 3 x + 9$

Step 2

Solve $10 x - 2 = 3 x + 9$ for $x$ .

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Step 2.1

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

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Step 2.1.1

Subtract $3 x$ from both sides of the equation.

$10 x - 2 - 3 x = 9$

Step 2.1.2

Subtract $3 x$ from $10 x$ .

$7 x - 2 = 9$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the equation.

$7 x = 9 + 2$

Step 2.2.2

Add $9$ and $2$ .

$7 x = 11$

Step 2.3

Divide each term in $7 x = 11$ by $7$ and simplify.

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Step 2.3.1

Divide each term in $7 x = 11$ by $7$ .

$\frac{7 x}{7} = \frac{11}{7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{11}{7}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{7}$

Step 3

Evaluate $y$ when $x = \frac{11}{7}$ .

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Step 3.1

Substitute $\frac{11}{7}$ for $x$ .

$y = 3 (\frac{11}{7}) + 9$

Step 3.2

Simplify $3 (\frac{11}{7}) + 9$ .

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Step 3.2.1

Multiply $3 (\frac{11}{7})$ .

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Step 3.2.1.1

Combine $3$ and $\frac{11}{7}$ .

$y = \frac{3 \cdot 11}{7} + 9$

Step 3.2.1.2

Multiply $3$ by $11$ .

$y = \frac{33}{7} + 9$

Step 3.2.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = \frac{33}{7} + 9 \cdot \frac{7}{7}$

Step 3.2.3

Combine $9$ and $\frac{7}{7}$ .

$y = \frac{33}{7} + \frac{9 \cdot 7}{7}$

Step 3.2.4

Combine the numerators over the common denominator.

$y = \frac{33 + 9 \cdot 7}{7}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $9$ by $7$ .

$y = \frac{33 + 63}{7}$

Step 3.2.5.2

Add $33$ and $63$ .

$y = \frac{96}{7}$

Step 4

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

$(\frac{11}{7}, \frac{96}{7})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{11}{7}, \frac{96}{7})$

Equation Form:

$x = \frac{11}{7}, y = \frac{96}{7}$

Step 6