Algebra Examples

$\frac{3}{5} x + \frac{1}{3} y = \frac{1}{15}$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$\frac{3}{5} x + \frac{1}{3} \cdot (0) = \frac{1}{15}$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $\frac{3}{5} x + \frac{1}{3} \cdot (0)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

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

$\frac{3 x}{5} + \frac{1}{3} \cdot (0) = \frac{1}{15}$

Step 1.2.1.1.2

Multiply $\frac{1}{3}$ by $0$ .

$\frac{3 x}{5} + 0 = \frac{1}{15}$

Step 1.2.1.2

Add $\frac{3 x}{5}$ and $0$ .

$\frac{3 x}{5} = \frac{1}{15}$

Step 1.2.2

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

$\frac{5}{3} \cdot \frac{3 x}{5} = \frac{5}{3} \cdot \frac{1}{15}$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

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

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Step 1.2.3.1.1.1

Cancel the common factor of $5$ .

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Step 1.2.3.1.1.1.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 x}{5} = \frac{5}{3} \cdot \frac{1}{15}$

Step 1.2.3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{5}{3} \cdot \frac{1}{15}$

Step 1.2.3.1.1.2

Cancel the common factor of $3$ .

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Step 1.2.3.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{5}{3} \cdot \frac{1}{15}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{5}{3} \cdot \frac{1}{15}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{5}{3} \cdot \frac{1}{15}$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Simplify $\frac{5}{3} \cdot \frac{1}{15}$ .

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Step 1.2.3.2.1.1

Cancel the common factor of $5$ .

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Step 1.2.3.2.1.1.1

Factor $5$ out of $15$ .

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

Step 1.2.3.2.1.1.2

Cancel the common factor.

$x = \frac{5}{3} \cdot \frac{1}{5 \cdot 3}$

Step 1.2.3.2.1.1.3

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{1}{3}$

Step 1.2.3.2.1.2

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

$x = \frac{1}{3 \cdot 3}$

Step 1.2.3.2.1.3

Multiply $3$ by $3$ .

$x = \frac{1}{9}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{9}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$\frac{3}{5} \cdot (0) + \frac{1}{3} y = \frac{1}{15}$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $\frac{3}{5} \cdot (0) + \frac{1}{3} y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $\frac{3}{5}$ by $0$ .

$0 + \frac{1}{3} y = \frac{1}{15}$

Step 2.2.1.1.2

Combine $\frac{1}{3}$ and $y$ .

$0 + \frac{y}{3} = \frac{1}{15}$

Step 2.2.1.2

Add $0$ and $\frac{y}{3}$ .

$\frac{y}{3} = \frac{1}{15}$

Step 2.2.2

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (\frac{1}{15})$

Step 2.2.3

Simplify both sides of the equation.

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Step 2.2.3.1

Simplify the left side.

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Step 2.2.3.1.1

Cancel the common factor of $3$ .

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Step 2.2.3.1.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 (\frac{1}{15})$

Step 2.2.3.1.1.2

Rewrite the expression.

$y = 3 (\frac{1}{15})$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Cancel the common factor of $3$ .

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Step 2.2.3.2.1.1

Factor $3$ out of $15$ .

$y = 3 \frac{1}{3 (5)}$

Step 2.2.3.2.1.2

Cancel the common factor.

$y = 3 \frac{1}{3 \cdot 5}$

Step 2.2.3.2.1.3

Rewrite the expression.

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{5})$

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{9}, 0)$

y-intercept(s): $(0, \frac{1}{5})$

Step 4