Algebra Examples

$y = \frac{5}{2} x + 9$ $y = \frac{1}{2} x + 1$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{5}{2} x + 9 = \frac{1}{2} x + 1$

Step 2

Solve $\frac{5}{2} x + 9 = \frac{1}{2} x + 1$ for $x$ .

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Step 2.1

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

$\frac{5 x}{2} + 9 = \frac{1}{2} x + 1$

Step 2.2

Combine $\frac{1}{2}$ and $x$ .

$\frac{5 x}{2} + 9 = \frac{x}{2} + 1$

Step 2.3

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

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Step 2.3.1

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{5 x}{2} + 9 - \frac{x}{2} = 1$

Step 2.3.2

Combine the numerators over the common denominator.

$9 + \frac{5 x - x}{2} = 1$

Step 2.3.3

Subtract $x$ from $5 x$ .

$9 + \frac{4 x}{2} = 1$

Step 2.3.4

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

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Step 2.3.4.1

Factor $2$ out of $4 x$ .

$9 + \frac{2 (2 x)}{2} = 1$

Step 2.3.4.2

Cancel the common factors.

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Step 2.3.4.2.1

Factor $2$ out of $2$ .

$9 + \frac{2 (2 x)}{2 (1)} = 1$

Step 2.3.4.2.2

Cancel the common factor.

$9 + \frac{2 (2 x)}{2 \cdot 1} = 1$

Step 2.3.4.2.3

Rewrite the expression.

$9 + \frac{2 x}{1} = 1$

Step 2.3.4.2.4

Divide $2 x$ by $1$ .

$9 + 2 x = 1$

Step 2.4

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

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Step 2.4.1

Subtract $9$ from both sides of the equation.

$2 x = 1 - 9$

Step 2.4.2

Subtract $9$ from $1$ .

$2 x = - 8$

Step 2.5

Divide each term in $2 x = - 8$ by $2$ and simplify.

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Step 2.5.1

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $2$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $- 8$ by $2$ .

$x = - 4$

Step 3

Evaluate $y$ when $x = - 4$ .

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Step 3.1

Substitute $- 4$ for $x$ .

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

Step 3.2

Substitute $- 4$ for $x$ in $y = \frac{1}{2} \cdot (- 4) + 1$ and solve for $y$ .

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Step 3.2.1

Multiply $\frac{1}{2}$ by $- 4$ .

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

Step 3.2.2

Simplify $\frac{1}{2} \cdot - 4 + 1$ .

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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

Factor $2$ out of $- 4$ .

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

Step 3.2.2.1.2

Cancel the common factor.

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

Step 3.2.2.1.3

Rewrite the expression.

$y = - 2 + 1$

Step 3.2.2.2

Add $- 2$ and $1$ .

$y = - 1$

Step 4

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

$(- 4, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Step 6