Pre-Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

$- 3 x - 3 = x + 2$

Step 2

Solve $- 3 x - 3 = x + 2$ 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 $x$ from both sides of the equation.

$- 3 x - 3 - x = 2$

Step 2.1.2

Subtract $x$ from $- 3 x$ .

$- 4 x - 3 = 2$

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 $3$ to both sides of the equation.

$- 4 x = 2 + 3$

Step 2.2.2

Add $2$ and $3$ .

$- 4 x = 5$

Step 2.3

Divide each term in $- 4 x = 5$ by $- 4$ and simplify.

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Step 2.3.1

Divide each term in $- 4 x = 5$ by $- 4$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 4$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

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

Step 3

Evaluate $y$ when $x = - \frac{5}{4}$ .

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Step 3.1

Substitute $- \frac{5}{4}$ for $x$ .

$y = (- \frac{5}{4}) + 2$

Step 3.2

Substitute $- \frac{5}{4}$ for $x$ in $y = (- \frac{5}{4}) + 2$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = - \frac{5}{4} + 2$

Step 3.2.2

Remove parentheses.

$y = (- \frac{5}{4}) + 2$

Step 3.2.3

Simplify $(- \frac{5}{4}) + 2$ .

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Step 3.2.3.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3.2.3.2

Combine $2$ and $\frac{4}{4}$ .

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

Step 3.2.3.3

Combine the numerators over the common denominator.

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

Step 3.2.3.4

Simplify the numerator.

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Step 3.2.3.4.1

Multiply $2$ by $4$ .

$y = \frac{- 5 + 8}{4}$

Step 3.2.3.4.2

Add $- 5$ and $8$ .

$y = \frac{3}{4}$

Step 4

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

$(- \frac{5}{4}, \frac{3}{4})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{5}{4}, \frac{3}{4})$

Equation Form:

$x = - \frac{5}{4}, y = \frac{3}{4}$

Step 6