Chapter 2: Q. 1.125 (page 271)

_{Solve the formula $3 x + 4 y = 10$ for y: ⓐ when $x = \frac{14}{3}$ ⓑ in general}

Short Answer

Expert verified

$a . Thesimplifiedvalueisy=-1$

$Ingeneral y = \frac{10 - 3 x}{4}$

Step by step solution

Step 1. Given information

The given equation is $3 x + 4 y = 10$

We have to solve the given equation when $x = \frac{14}{3}$

Step 2. Explanation

$\begin{array}{l} Solve: 3 x + 4 y = 10 \\ \Rightarrow 3 (\frac{14}{3}) + 4 y = 10 (Substitute) \\ \Rightarrow 14 + 4 y = 10 (Simplify) \\ \Rightarrow 14 - 14 + 4 y = 10 - 14 (Subtract14toisolatetheyterm) \\ \Rightarrow 4 y = - 4 (Simplify) \\ \Rightarrow \frac{4 y}{4} = \frac{- 4}{4} (Divide) \\ \Rightarrow y = - 1 (Simplify) \\ Thesimplifiedvalueisy=-1 \end{array}$

Step 3. Part b. Explanation

$\begin{array}{l} Ingeneral \\ 3 x + 4 y = 10 \\ \Rightarrow 3 x - 3 x + 4 y = 10 - 3 x (Subtract3xtoisolatetheyterm) \\ \Rightarrow \frac{4 y}{4} = \frac{10 - 3 x}{4} (Divide) \\ \Rightarrow y = \frac{10 - 3 x}{4} (Simplify) \\ Ingeneral y = \frac{10 - 3 x}{4} \end{array}$

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_{Solve the formula $3 x + 4 y = 10$ for y: ⓐ when $x = \frac{14}{3}$ ⓑ in general}

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Part b. Explanation

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Solve the formula 3x+4y=10for y: ⓐ when x=143ⓑ in general

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Part b. Explanation

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_{Solve the formula $3 x + 4 y = 10$ for y: ⓐ when $x = \frac{14}{3}$ ⓑ in general}