Algebra Examples

$y = \frac{7}{6} x + 2$ $y = - 5$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{7}{6} x + 2 = - 5$

Step 2

Solve $\frac{7}{6} x + 2 = - 5$ for $x$ .

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Step 2.1

Combine $\frac{7}{6}$ and $x$ .

$\frac{7 x}{6} + 2 = - 5$

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$\frac{7 x}{6} = - 5 - 2$

Step 2.2.2

Subtract $2$ from $- 5$ .

$\frac{7 x}{6} = - 7$

Step 2.3

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 x}{6} = \frac{6}{7} \cdot - 7$

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $\frac{6}{7} \cdot \frac{7 x}{6}$ .

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Step 2.4.1.1.1

Cancel the common factor of $6$ .

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Step 2.4.1.1.1.1

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 x}{6} = \frac{6}{7} \cdot - 7$

Step 2.4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot - 7$

Step 2.4.1.1.2

Cancel the common factor of $7$ .

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Step 2.4.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{6}{7} \cdot - 7$

Step 2.4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot - 7$

Step 2.4.1.1.2.3

Rewrite the expression.

$x = \frac{6}{7} \cdot - 7$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $\frac{6}{7} \cdot - 7$ .

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Step 2.4.2.1.1

Cancel the common factor of $7$ .

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Step 2.4.2.1.1.1

Factor $7$ out of $- 7$ .

$x = \frac{6}{7} \cdot (7 (- 1))$

Step 2.4.2.1.1.2

Cancel the common factor.

$x = \frac{6}{7} \cdot (7 \cdot - 1)$

Step 2.4.2.1.1.3

Rewrite the expression.

$x = 6 \cdot - 1$

Step 2.4.2.1.2

Multiply $6$ by $- 1$ .

$x = - 6$

Step 3

Substitute $- 6$ for $x$ .

$y = - 5$

Step 4

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

$(- 6, - 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 6, - 5)$

Equation Form:

$x = - 6, y = - 5$

Step 6