Algebra Examples

$y = 2$ $y = \frac{5}{2} x - 3$

Step 1

Eliminate the equal sides of each equation and combine.

$2 = \frac{5}{2} x - 3$

Step 2

Solve $2 = \frac{5}{2} x - 3$ for $x$ .

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Step 2.1

Rewrite the equation as $\frac{5}{2} x - 3 = 2$ .

$\frac{5}{2} x - 3 = 2$

Step 2.2

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

$\frac{5 x}{2} - 3 = 2$

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 $3$ to both sides of the equation.

$\frac{5 x}{2} = 2 + 3$

Step 2.3.2

Add $2$ and $3$ .

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

Step 2.4

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

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

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 $\frac{2}{5} \cdot \frac{5 x}{2}$ .

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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

Cancel the common factor.

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

Step 2.5.1.1.1.2

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 2.5.2

Simplify the right side.

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Step 2.5.2.1

Cancel the common factor of $5$ .

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Step 2.5.2.1.1

Cancel the common factor.

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

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 $x$ .

$y = \frac{5}{2} \cdot (2) - 3$

Step 3.2

Substitute $2$ for $x$ in $y = \frac{5}{2} \cdot (2) - 3$ and solve for $y$ .

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Step 3.2.1

Multiply $\frac{5}{2}$ by $2$ .

$y = \frac{5}{2} \cdot 2 - 3$

Step 3.2.2

Simplify $\frac{5}{2} \cdot 2 - 3$ .

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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

Cancel the common factor.

$y = \frac{5}{2} \cdot 2 - 3$

Step 3.2.2.1.2

Rewrite the expression.

$y = 5 - 3$

Step 3.2.2.2

Subtract $3$ from $5$ .

$y = 2$

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