Algebra Examples

$y = 3 x - 4$ $y = - \frac{1}{2} x + 3$

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

Solve $3 x - 4 = - \frac{1}{2} x + 3$ for $x$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify each term.

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Step 2.2.5.1

Simplify the numerator.

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Step 2.2.5.1.1

Factor $x$ out of $3 x \cdot 2 + x$ .

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Step 2.2.5.1.1.1

Factor $x$ out of $3 x \cdot 2$ .

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

Step 2.2.5.1.1.2

Raise $x$ to the power of $1$ .

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

Step 2.2.5.1.1.3

Factor $x$ out of $x^{1}$ .

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

Step 2.2.5.1.1.4

Factor $x$ out of $x (3 \cdot 2) + x \cdot 1$ .

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

Step 2.2.5.1.2

Multiply $3$ by $2$ .

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

Step 2.2.5.1.3

Add $6$ and $1$ .

$\frac{x \cdot 7}{2} - 4 = 3$

Step 2.2.5.2

Move $7$ to the left of $x$ .

$\frac{7 x}{2} - 4 = 3$

Step 2.3

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

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Step 2.3.1

Add $4$ to both sides of the equation.

$\frac{7 x}{2} = 3 + 4$

Step 2.3.2

Add $3$ and $4$ .

$\frac{7 x}{2} = 7$

Step 2.4

Multiply both sides of the equation by $\frac{2}{7}$ .

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 7$

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 $\frac{2}{7} \cdot \frac{7 x}{2}$ .

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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

Cancel the common factor.

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 7$

Step 2.5.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 7$

Step 2.5.1.1.2

Cancel the common factor of $7$ .

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Step 2.5.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{2}{7} \cdot 7$

Step 2.5.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 7$

Step 2.5.1.1.2.3

Rewrite the expression.

$x = \frac{2}{7} \cdot 7$

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

Cancel the common factor of $7$ .

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Step 2.5.2.1.1

Cancel the common factor.

$x = \frac{2}{7} \cdot 7$

Step 2.5.2.1.2

Rewrite the expression.

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

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Step 3.1

Substitute $2$ for $x$ .

$y = - \frac{1}{2} \cdot 2 + 3$

Step 3.2

Substitute $2$ for $x$ in $y = - \frac{1}{2} \cdot 2 + 3$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = - \frac{1}{2} \cdot 2 + 3$

Step 3.2.2

Simplify $- \frac{1}{2} \cdot 2 + 3$ .

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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 $- \frac{1}{2}$ into the numerator.

$y = \frac{- 1}{2} \cdot 2 + 3$

Step 3.2.2.1.2

Cancel the common factor.

$y = \frac{- 1}{2} \cdot 2 + 3$

Step 3.2.2.1.3

Rewrite the expression.

$y = - 1 + 3$

Step 3.2.2.2

Add $- 1$ and $3$ .

$y = 2$

Step 4

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

$(2, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 2)$

Equation Form:

$x = 2, y = 2$

Step 6