Chapter 4: Q54. (page 166)

Solve each system by using substitution or elimination.
$\begin{array}{l} 3 p + 6 q = - 3 \\ 2 p - 3 q = - 9 \end{array}$

Short Answer

Expert verified

The solution of the system of equations: $\begin{matrix} 3 p + 6 q = - 3 \\ 2 p - 3 q = - 9 \end{matrix}$ is $(- 3, 1)$ .

Step by step solution

- Solve the first equation for p in terms of q

Write the equation $3 p + 6 q = - 3$ in terms of p.

$\begin{matrix} 3 p + 6 q = - 3 \\ 3 p + 6 q - 6 q = - 3 - 6 q \\ 3 p = - 3 - 6 q \\ \frac{3 p}{3} = \frac{- 3 - 6 q}{3} \\ p = - 1 - 2 q \end{matrix}$

- Solve for q

Substitute $- 1 - 2 q$ for p into equation $2 p - 3 q = - 9$ so as to obtain the value of q.

$\begin{matrix} 2 (- 1 - 2 q) - 3 q = - 9 \\ 2 (- 1) - 2 (2 q) - 3 q = - 9 \\ - 2 - 4 q - 3 q = - 9 \\ - 2 - 7 q + 2 = - 9 + 2 \\ - 7 q = - 7 \\ q = 1 \end{matrix}$

- Solve for p

Now substitute 1 for q into either original equation and solve for p.

$\begin{matrix} 3 p + 6 (1) = - 3 \\ 3 p + 6 - 6 = - 3 - 6 \\ 3 p = - 9 \\ p = - 3 \end{matrix}$

Therefore, the solution of the system is $(- 3, 1)$ .

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Solve each system by using substitution or elimination.
$\begin{array}{l} 3 p + 6 q = - 3 \\ 2 p - 3 q = - 9 \end{array}$

Short Answer

Step by step solution

- Solve the first equation for p in terms of q

- Solve for q

- Solve for p

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Solve each system by using substitution or elimination.3p+6q=−32p−3q=−9

Short Answer

Step by step solution

- Solve the first equation for p in terms of q

- Solve for q

- Solve for p

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Solve each system by using substitution or elimination.
$\begin{array}{l} 3 p + 6 q = - 3 \\ 2 p - 3 q = - 9 \end{array}$