Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

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.

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

Step 2.3.2

Combine the numerators over the common denominator.

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

Step 2.3.3

Subtract $x$ from $3 x$ .

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

Step 2.3.4

Cancel the common factor of $2$ .

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Step 2.3.4.1

Cancel the common factor.

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

Step 2.3.4.2

Divide $x$ by $1$ .

$2 + x = 4$

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 $2$ from both sides of the equation.

$x = 4 - 2$

Step 2.4.2

Subtract $2$ from $4$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

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Step 3.1

Substitute $2$ for $x$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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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

Cancel the common factor.

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

Step 3.2.2.1.2

Rewrite the expression.

$y = 1 + 4$

Step 3.2.2.2

Add $1$ and $4$ .

$y = 5$

Step 4

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

$(2, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Step 6