Algebra Examples

$y = - 1$ $y = - \frac{5}{2} x + 4$

Step 1

Eliminate the equal sides of each equation and combine.

$- 1 = - \frac{5}{2} x + 4$

Step 2

Solve $- 1 = - \frac{5}{2} x + 4$ for $x$ .

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Step 2.1

Rewrite the equation as $- \frac{5}{2} x + 4 = - 1$ .

$- \frac{5}{2} x + 4 = - 1$

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $x$ and $\frac{5}{2}$ .

$- \frac{x \cdot 5}{2} + 4 = - 1$

Step 2.2.2

Move $5$ to the left of $x$ .

$- \frac{5 x}{2} + 4 = - 1$

Step 2.3

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

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Step 2.3.1

Subtract $4$ from both sides of the equation.

$- \frac{5 x}{2} = - 1 - 4$

Step 2.3.2

Subtract $4$ from $- 1$ .

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

Step 2.4

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

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

Step 2.5

Simplify both sides of the equation.

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Step 2.5.1

Simplify the left side.

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Step 2.5.1.1

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

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Step 2.5.1.1.1

Cancel the common factor of $2$ .

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Step 2.5.1.1.1.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

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

Step 2.5.1.1.1.2

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

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

Step 2.5.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 2.5.1.1.1.4

Cancel the common factor.

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

Step 2.5.1.1.1.5

Rewrite the expression.

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

Step 2.5.1.1.2

Cancel the common factor of $5$ .

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Step 2.5.1.1.2.1

Factor $5$ out of $- 5 x$ .

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

Step 2.5.1.1.2.2

Cancel the common factor.

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

Step 2.5.1.1.2.3

Rewrite the expression.

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

Step 2.5.1.1.3

Multiply.

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Step 2.5.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.5.1.1.3.2

Multiply $x$ by $1$ .

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

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

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

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Step 2.5.2.1.1

Cancel the common factor of $5$ .

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Step 2.5.2.1.1.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

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

Step 2.5.2.1.1.2

Factor $5$ out of $- 5$ .

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

Step 2.5.2.1.1.3

Cancel the common factor.

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

Step 2.5.2.1.1.4

Rewrite the expression.

$x = - 2 \cdot - 1$

Step 2.5.2.1.2

Multiply $- 2$ by $- 1$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

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Step 3.1

Substitute $2$ for $x$ .

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

Step 3.2

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

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Step 3.2.1

Remove parentheses.

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

Step 3.2.2

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

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Step 3.2.2.1.2

Cancel the common factor.

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

Step 3.2.2.1.3

Rewrite the expression.

$y = - 5 + 4$

Step 3.2.2.2

Add $- 5$ and $4$ .

$y = - 1$

Step 4

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

$(2, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 6