Chapter 4: Q55. (page 166)

Solve each system by using substitution or elimination.
$\begin{matrix} a + 5 b = 1 \\ 7 a - 2 b = 44 \end{matrix}$

Short Answer

Expert verified

The solution of the system of equations: $\begin{matrix} a + 5 b = 1 \\ 7 a - 2 b = 44 \end{matrix}$ is $(6, - 1)$ .

Step by step solution

- Solve the first equation for a in terms of b

Write the first equation $a + 5 b = 1$ for a in terms of b.

$\begin{matrix} a + 5 b = 1 \\ a + 5 b - 5 b = 1 - 5 b \\ a = 1 - 5 b \end{matrix}$

- Solve for b

Substitute $1 - 5 b$ for a into equation $7 a - 2 b = 44$ so as to obtain the value of b.

$\begin{matrix} 7 (1 - 5 b) - 2 b = 44 \\ 7 (1) - 7 (5 b) - 2 b = 44 \\ 7 - 35 b - 2 b = 44 \\ 7 - 37 b - 7 = 44 - 7 \\ - 37 b = 37 \\ b = - 1 \end{matrix}$

- Solve for a

Now substitute -1 for b into either original equation and solve for a.

$\begin{matrix} a + 5 (- 1) = 1 \\ a - 5 + 5 = 1 + 5 \\ a = 6 \end{matrix}$

Therefore, the solution of the system is $(6, - 1)$ .

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Solve each system by using substitution or elimination.
$\begin{matrix} a + 5 b = 1 \\ 7 a - 2 b = 44 \end{matrix}$

Short Answer

Step by step solution

- Solve the first equation for a in terms of b

- Solve for b

- Solve for a

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Solve each system by using substitution or elimination.a+5b=17a−2b=44

Short Answer

Step by step solution

- Solve the first equation for a in terms of b

- Solve for b

- Solve for a

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Solve each system by using substitution or elimination.
$\begin{matrix} a + 5 b = 1 \\ 7 a - 2 b = 44 \end{matrix}$