Chapter 4: Q50. (page 166)

Solve each system of equations.
$\begin{array}{l} 2 a + b = 2 \\ 5 a = 15 \\ a + b + c = - 1 \end{array}$

Short Answer

Expert verified

The solution of the system of equations: $\begin{matrix} 2 a + b = 2 \\ 5 a = 15 \\ a + b + c = - 1 \end{matrix}$ is $(3, - 4, 0) .$

Step by step solution

- Solve for variables a

Let the equations be:

$2 a + b = 2$ … (i)

$5 a = 15$ … (ii)

$a + b + c = - 1$ … (iii)

Solve equation (ii) so as to obtain variable a.

$\begin{matrix} \frac{5 a}{5} = \frac{15}{5} \\ a = 3 \end{matrix}$

- Solve for variable b

Substitute 3 for a into equation (i) so as to obtain the value of b.

$\begin{matrix} 2 (3) + b = 2 \\ 6 + b - 6 = 2 - 6 \\ b = - 4 \end{matrix}$

- Solve for variable c

Now substitute 3 for a and -4 for b into the equation (iii) so as to obtain variable c.

$\begin{matrix} (3) + (- 4) + c = - 1 \\ 3 - 4 + c = - 1 \\ - 1 + c + 1 = - 1 + 1 \\ c = 0 \end{matrix}$

Therefore, the solution is $(3, - 4, 0)$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each system of equations.
$\begin{array}{l} 2 a + b = 2 \\ 5 a = 15 \\ a + b + c = - 1 \end{array}$

Short Answer

Step by step solution

- Solve for variables a

- Solve for variable b

- Solve for variable c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations.2a+b=25a=15a+b+c=−1

Short Answer

Step by step solution

- Solve for variables a

- Solve for variable b

- Solve for variable c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{array}{l} 2 a + b = 2 \\ 5 a = 15 \\ a + b + c = - 1 \end{array}$