Algebra Examples

$y = \frac{3}{5} x - 1$ $y = \frac{2}{5} x$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{3}{5} x - 1 = \frac{2}{5} x$

Step 2

Solve $\frac{3}{5} x - 1 = \frac{2}{5} x$ for $x$ .

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Step 2.1

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} - 1 = \frac{2}{5} x$

Step 2.2

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

$\frac{3 x}{5} - 1 = \frac{2 x}{5}$

Step 2.3

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

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Step 2.3.1

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

$\frac{3 x}{5} - 1 - \frac{2 x}{5} = 0$

Step 2.3.2

Combine the numerators over the common denominator.

$- 1 + \frac{3 x - 2 x}{5} = 0$

Step 2.3.3

Subtract $2 x$ from $3 x$ .

$- 1 + \frac{x}{5} = 0$

Step 2.4

Add $1$ to both sides of the equation.

$\frac{x}{5} = 1$

Step 2.5

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot 1$

Step 2.6

Simplify both sides of the equation.

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Step 2.6.1

Simplify the left side.

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Step 2.6.1.1

Cancel the common factor of $5$ .

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Step 2.6.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot 1$

Step 2.6.1.1.2

Rewrite the expression.

$x = 5 \cdot 1$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

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

Cancel the common factor of $5$ .

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Step 3.2.2.1

Cancel the common factor.

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

Step 3.2.2.2

Rewrite the expression.

$y = 2$

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