Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

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

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Step 2.1

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

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Step 2.1.1

Rewrite.

$x + 3 = 0 + 0 + \frac{2}{5} x$

Step 2.1.2

Simplify by adding zeros.

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

Step 2.1.3

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

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

Step 2.2

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

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Step 2.2.1

Subtract $\frac{2 x}{5}$ from both sides of the equation.

$x + 3 - \frac{2 x}{5} = 0$

Step 2.2.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x \cdot \frac{5}{5} - \frac{2 x}{5} + 3 = 0$

Step 2.2.3

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

$\frac{x \cdot 5}{5} - \frac{2 x}{5} + 3 = 0$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - 2 x}{5} + 3 = 0$

Step 2.2.5

Subtract $2 x$ from $x \cdot 5$ .

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Step 2.2.5.1

Reorder $x$ and $5$ .

$\frac{5 \cdot x - 2 x}{5} + 3 = 0$

Step 2.2.5.2

Subtract $2 x$ from $5 \cdot x$ .

$\frac{3 \cdot x}{5} + 3 = 0$

$\frac{3 x}{5} + 3 = 0$

Step 2.3

Subtract $3$ from both sides of the equation.

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

Step 2.4

Multiply both sides of the equation by $\frac{5}{3}$ .

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

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 $\frac{5}{3} \cdot \frac{3 x}{5}$ .

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Step 2.5.1.1.1

Cancel the common factor of $5$ .

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Step 2.5.1.1.1.1

Cancel the common factor.

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

Step 2.5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{5}{3} \cdot - 3$

Step 2.5.1.1.2

Cancel the common factor of $3$ .

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Step 2.5.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{5}{3} \cdot - 3$

Step 2.5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{5}{3} \cdot - 3$

Step 2.5.1.1.2.3

Rewrite the expression.

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

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

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

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Step 2.5.2.1.1

Cancel the common factor of $3$ .

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Step 2.5.2.1.1.1

Factor $3$ out of $- 3$ .

$x = \frac{5}{3} \cdot (3 (- 1))$

Step 2.5.2.1.1.2

Cancel the common factor.

$x = \frac{5}{3} \cdot (3 \cdot - 1)$

Step 2.5.2.1.1.3

Rewrite the expression.

$x = 5 \cdot - 1$

Step 2.5.2.1.2

Multiply $5$ by $- 1$ .

$x = - 5$

Step 3

Evaluate $y$ when $x = - 5$ .

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Step 3.1

Substitute $- 5$ for $x$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Factor $5$ out of $- 5$ .

$y = \frac{2}{5} \cdot (5 (- 1))$

Step 3.2.2.1.2

Cancel the common factor.

$y = \frac{2}{5} \cdot (5 \cdot - 1)$

Step 3.2.2.1.3

Rewrite the expression.

$y = 2 \cdot - 1$

Step 3.2.2.2

Multiply $2$ by $- 1$ .

$y = - 2$

Step 4

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

$(- 5, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 5, - 2)$

Equation Form:

$x = - 5, y = - 2$

Step 6