Algebra Examples

$y = - \frac{3}{2} x - 4$ $x - y = - 6$

Step 1

Simplify each term.

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Step 1.1

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

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

$x - y = - 6$

Step 1.2

Move $3$ to the left of $x$ .

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

$x - y = - 6$

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

$x - y = - 6$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $x - y = - 6$ with $- \frac{3 x}{2} - 4$ .

$x - (- \frac{3 x}{2} - 4) = - 6$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$x + \frac{3 x}{2} + 4 = - 6$

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

Step 2.2.1.1.2

Multiply $- - \frac{3 x}{2}$ .

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Step 2.2.1.1.2.1

Multiply $- 1$ by $- 1$ .

$x + 1 (\frac{3 x}{2}) + 4 = - 6$

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

Step 2.2.1.1.2.2

Multiply $\frac{3 x}{2}$ by $1$ .

$x + \frac{3 x}{2} + 4 = - 6$

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

$x + \frac{3 x}{2} + 4 = - 6$

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

Step 2.2.1.1.3

Multiply $- 1$ by $- 4$ .

$x + \frac{3 x}{2} + 4 = - 6$

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

$x + \frac{3 x}{2} + 4 = - 6$

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

Step 2.2.1.2

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

$x \cdot \frac{2}{2} + \frac{3 x}{2} + 4 = - 6$

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

Step 2.2.1.3

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

$\frac{x \cdot 2}{2} + \frac{3 x}{2} + 4 = - 6$

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

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 x}{2} + 4 = - 6$

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

Step 2.2.1.5

Add $x \cdot 2$ and $3 x$ .

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Step 2.2.1.5.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x + 3 x}{2} + 4 = - 6$

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

Step 2.2.1.5.2

Add $2 \cdot x$ and $3 x$ .

$\frac{5 \cdot x}{2} + 4 = - 6$

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

$\frac{5 x}{2} + 4 = - 6$

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

$\frac{5 x}{2} + 4 = - 6$

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

$\frac{5 x}{2} + 4 = - 6$

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

$\frac{5 x}{2} + 4 = - 6$

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

Step 3

Solve for $x$ in $\frac{5 x}{2} + 4 = - 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4$ from both sides of the equation.

$\frac{5 x}{2} = - 6 - 4$

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

Step 3.1.2

Subtract $4$ from $- 6$ .

$\frac{5 x}{2} = - 10$

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

$\frac{5 x}{2} = - 10$

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

Step 3.2

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot - 10$

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

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{2}{5} \cdot \frac{5 x}{2}$ .

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Step 3.3.1.1.1

Cancel the common factor of $2$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot - 10$

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

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 10$

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

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 10$

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

Step 3.3.1.1.2

Cancel the common factor of $5$ .

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Step 3.3.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} \cdot (5 (x)) = \frac{2}{5} \cdot - 10$

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

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 10$

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

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{2}{5} \cdot - 10$

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

$x = \frac{2}{5} \cdot - 10$

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

$x = \frac{2}{5} \cdot - 10$

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

$x = \frac{2}{5} \cdot - 10$

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

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{2}{5} \cdot - 10$ .

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Step 3.3.2.1.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1.1

Factor $5$ out of $- 10$ .

$x = \frac{2}{5} \cdot (5 (- 2))$

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

Step 3.3.2.1.1.2

Cancel the common factor.

$x = \frac{2}{5} \cdot (5 \cdot - 2)$

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

Step 3.3.2.1.1.3

Rewrite the expression.

$x = 2 \cdot - 2$

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

$x = 2 \cdot - 2$

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

Step 3.3.2.1.2

Multiply $2$ by $- 2$ .

$x = - 4$

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

$x = - 4$

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

$x = - 4$

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

$x = - 4$

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

$x = - 4$

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

Step 4

Replace all occurrences of $x$ with $- 4$ in each equation.

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Step 4.1

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

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

$x = - 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Cancel the common factor of $- 4$ and $2$ .

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Step 4.2.1.1.1.1

Factor $2$ out of $3 (- 4)$ .

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

$x = - 4$

Step 4.2.1.1.1.2

Cancel the common factors.

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Step 4.2.1.1.1.2.1

Factor $2$ out of $2$ .

$y = - \frac{2 (3 \cdot (- 2))}{2 (1)} - 4$

$x = - 4$

Step 4.2.1.1.1.2.2

Cancel the common factor.

$y = - \frac{2 (3 \cdot (- 2))}{2 \cdot 1} - 4$

$x = - 4$

Step 4.2.1.1.1.2.3

Rewrite the expression.

$y = - \frac{3 \cdot (- 2)}{1} - 4$

$x = - 4$

Step 4.2.1.1.1.2.4

Divide $3 \cdot (- 2)$ by $1$ .

$y = - (3 \cdot (- 2)) - 4$

$x = - 4$

$y = - (3 \cdot (- 2)) - 4$

$x = - 4$

$y = - (3 \cdot (- 2)) - 4$

$x = - 4$

Step 4.2.1.1.2

Multiply $- (3 \cdot (- 2))$ .

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Step 4.2.1.1.2.1

Multiply $3$ by $- 2$ .

$y = 6 - 4$

$x = - 4$

Step 4.2.1.1.2.2

Multiply $- 1$ by $- 6$ .

$y = 6 - 4$

$x = - 4$

$y = 6 - 4$

$x = - 4$

$y = 6 - 4$

$x = - 4$

Step 4.2.1.2

Subtract $4$ from $6$ .

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

Step 5

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

$(- 4, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 2)$

Equation Form:

$x = - 4, y = 2$

Step 7