Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

Add $\frac{x}{2}$ to both sides of the equation.

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

Step 2.3.2

Combine the numerators over the common denominator.

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

Step 2.3.3

Add $x$ and $x$ .

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

Step 2.3.4

Cancel the common factor of $2$ .

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Step 2.3.4.1

Cancel the common factor.

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

Step 2.3.4.2

Divide $x$ by $1$ .

$1 + x = 9$

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 $1$ from both sides of the equation.

$x = 9 - 1$

Step 2.4.2

Subtract $1$ from $9$ .

$x = 8$

Step 3

Evaluate $y$ when $x = 8$ .

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Step 3.1

Substitute $8$ for $x$ .

$y = - \frac{1}{2} \cdot 8 + 9$

Step 3.2

Substitute $8$ for $x$ in $y = - \frac{1}{2} \cdot 8 + 9$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = - \frac{1}{2} \cdot 8 + 9$

Step 3.2.2

Simplify $- \frac{1}{2} \cdot 8 + 9$ .

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Step 3.2.2.1

Simplify each term.

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Step 3.2.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y = \frac{- 1}{2} \cdot 8 + 9$

Step 3.2.2.1.1.2

Factor $2$ out of $8$ .

$y = \frac{- 1}{2} \cdot (2 (4)) + 9$

Step 3.2.2.1.1.3

Cancel the common factor.

$y = \frac{- 1}{2} \cdot (2 \cdot 4) + 9$

Step 3.2.2.1.1.4

Rewrite the expression.

$y = - 1 \cdot 4 + 9$

Step 3.2.2.1.2

Multiply $- 1$ by $4$ .

$y = - 4 + 9$

Step 3.2.2.2

Add $- 4$ and $9$ .

$y = 5$

Step 4

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

$(8, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(8, 5)$

Equation Form:

$x = 8, y = 5$

Step 6