Precalculus Examples

$x + y = 30$ , $0.25 x + 0.5 y = 0.4 \cdot 30$

Step 1

Subtract $x$ from both sides of the equation.

$y = 30 - x$

$0.25 x + 0.5 y = 0.4 \cdot 30$

Step 2

Multiply $0.4$ by $30$ .

$0.25 x + 0.5 y = 12$

$y = 30 - x$

Step 3

Subtract $0.25 x$ from both sides of the equation.

$0.5 y = 12 - 0.25 x$

$y = 30 - x$

Step 4

Divide each term in $0.5 y = 12 - 0.25 x$ by $0.5$ and simplify.

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Step 4.1

Divide each term in $0.5 y = 12 - 0.25 x$ by $0.5$ .

$\frac{0.5 y}{0.5} = \frac{12}{0.5} + \frac{- 0.25 x}{0.5}$

$y = 30 - x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.5 y}{0.5} = \frac{12}{0.5} + \frac{- 0.25 x}{0.5}$

$y = 30 - x$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{0.5} + \frac{- 0.25 x}{0.5}$

$y = 30 - x$

$y = \frac{12}{0.5} + \frac{- 0.25 x}{0.5}$

$y = 30 - x$

$y = \frac{12}{0.5} + \frac{- 0.25 x}{0.5}$

$y = 30 - x$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Divide $12$ by $0.5$ .

$y = 24 + \frac{- 0.25 x}{0.5}$

$y = 30 - x$

Step 4.3.1.2

Move the negative in front of the fraction.

$y = 24 - \frac{0.25 x}{0.5}$

$y = 30 - x$

Step 4.3.1.3

Factor $0.25$ out of $0.25 x$ .

$y = 24 - \frac{0.25 (x)}{0.5}$

$y = 30 - x$

Step 4.3.1.4

Factor $0.5$ out of $0.5$ .

$y = 24 - \frac{0.25 (x)}{0.5 (1)}$

$y = 30 - x$

Step 4.3.1.5

Separate fractions.

$y = 24 - (\frac{0.25}{0.5} \cdot \frac{x}{1})$

$y = 30 - x$

Step 4.3.1.6

Divide $0.25$ by $0.5$ .

$y = 24 - (0.5 (\frac{x}{1}))$

$y = 30 - x$

Step 4.3.1.7

Cancel the common factor of $0.5$ .

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Step 4.3.1.7.1

Factor $0.5$ out of $1$ .

$y = 24 - (0.5 (\frac{x}{0.5 \cdot 2}))$

$y = 30 - x$

Step 4.3.1.7.2

Cancel the common factor.

$y = 24 - (0.5 (\frac{x}{0.5 \cdot 2}))$

$y = 30 - x$

Step 4.3.1.7.3

Rewrite the expression.

$y = 24 - \frac{x}{2}$

$y = 30 - x$

$y = 24 - \frac{x}{2}$

$y = 30 - x$

$y = 24 - \frac{x}{2}$

$y = 30 - x$

$y = 24 - \frac{x}{2}$

$y = 30 - x$

$y = 24 - \frac{x}{2}$

$y = 30 - x$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(12, 18)$

Step 6