Precalculus Examples

$0.5 a + 0.2 b = - 0.33$ , $- 0.4 a - 0.3 b = 0.18$ , $(- 0.9, 0.6)$

Step 1

Subtract $0.2 b$ from both sides of the equation.

$0.5 a = - 0.33 - 0.2 b$

$- 0.4 a - 0.3 b = 0.18$

Step 2

Divide each term in $0.5 a = - 0.33 - 0.2 b$ by $0.5$ and simplify.

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Step 2.1

Divide each term in $0.5 a = - 0.33 - 0.2 b$ by $0.5$ .

$\frac{0.5 a}{0.5} = \frac{- 0.33}{0.5} + \frac{- 0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.5 a}{0.5} = \frac{- 0.33}{0.5} + \frac{- 0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 0.33}{0.5} + \frac{- 0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

$a = \frac{- 0.33}{0.5} + \frac{- 0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

$a = \frac{- 0.33}{0.5} + \frac{- 0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $- 0.33$ by $0.5$ .

$a = - 0.66 + \frac{- 0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.2

Move the negative in front of the fraction.

$a = - 0.66 - \frac{0.2 b}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.3

Factor $0.2$ out of $0.2 b$ .

$a = - 0.66 - \frac{0.2 (b)}{0.5}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.4

Factor $0.5$ out of $0.5$ .

$a = - 0.66 - \frac{0.2 (b)}{0.5 (1)}$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.5

Separate fractions.

$a = - 0.66 - (\frac{0.2}{0.5} \cdot \frac{b}{1})$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.6

Divide $0.2$ by $0.5$ .

$a = - 0.66 - (0.4 (\frac{b}{1}))$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.7

Divide $b$ by $1$ .

$a = - 0.66 - (0.4 b)$

$- 0.4 a - 0.3 b = 0.18$

Step 2.3.1.8

Multiply $0.4$ by $- 1$ .

$a = - 0.66 - 0.4 b$

$- 0.4 a - 0.3 b = 0.18$

$a = - 0.66 - 0.4 b$

$- 0.4 a - 0.3 b = 0.18$

$a = - 0.66 - 0.4 b$

$- 0.4 a - 0.3 b = 0.18$

$a = - 0.66 - 0.4 b$

$- 0.4 a - 0.3 b = 0.18$

Step 3

Add $0.3 b$ to both sides of the equation.

$- 0.4 a = 0.18 + 0.3 b$

$a = - 0.66 - 0.4 b$

Step 4

Divide each term in $- 0.4 a = 0.18 + 0.3 b$ by $- 0.4$ and simplify.

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Step 4.1

Divide each term in $- 0.4 a = 0.18 + 0.3 b$ by $- 0.4$ .

$\frac{- 0.4 a}{- 0.4} = \frac{0.18}{- 0.4} + \frac{0.3 b}{- 0.4}$

$a = - 0.66 - 0.4 b$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 0.4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.4 a}{- 0.4} = \frac{0.18}{- 0.4} + \frac{0.3 b}{- 0.4}$

$a = - 0.66 - 0.4 b$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{0.18}{- 0.4} + \frac{0.3 b}{- 0.4}$

$a = - 0.66 - 0.4 b$

$a = \frac{0.18}{- 0.4} + \frac{0.3 b}{- 0.4}$

$a = - 0.66 - 0.4 b$

$a = \frac{0.18}{- 0.4} + \frac{0.3 b}{- 0.4}$

$a = - 0.66 - 0.4 b$

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 $0.18$ by $- 0.4$ .

$a = - 0.45 + \frac{0.3 b}{- 0.4}$

$a = - 0.66 - 0.4 b$

Step 4.3.1.2

Move the negative in front of the fraction.

$a = - 0.45 - \frac{0.3 b}{0.4}$

$a = - 0.66 - 0.4 b$

Step 4.3.1.3

Factor $0.3$ out of $0.3 b$ .

$a = - 0.45 - \frac{0.3 (b)}{0.4}$

$a = - 0.66 - 0.4 b$

Step 4.3.1.4

Factor $0.4$ out of $0.4$ .

$a = - 0.45 - \frac{0.3 (b)}{0.4 (1)}$

$a = - 0.66 - 0.4 b$

Step 4.3.1.5

Separate fractions.

$a = - 0.45 - (\frac{0.3}{0.4} \cdot \frac{b}{1})$

$a = - 0.66 - 0.4 b$

Step 4.3.1.6

Divide $0.3$ by $0.4$ .

$a = - 0.45 - (0.75 (\frac{b}{1}))$

$a = - 0.66 - 0.4 b$

Step 4.3.1.7

Divide $b$ by $1$ .

$a = - 0.45 - (0.75 b)$

$a = - 0.66 - 0.4 b$

Step 4.3.1.8

Multiply $0.75$ by $- 1$ .

$a = - 0.45 - 0.75 b$

$a = - 0.66 - 0.4 b$

$a = - 0.45 - 0.75 b$

$a = - 0.66 - 0.4 b$

$a = - 0.45 - 0.75 b$

$a = - 0.66 - 0.4 b$

$a = - 0.45 - 0.75 b$

$a = - 0.66 - 0.4 b$

Step 5

The ordered pair is a solution to the system of equations.

$(- 0.9, 0.6)$ is a solution