Chapter 3: Q5. (page 142)

Solve each system of equations.
$\begin{array}{l} 9 a + 7 b = - 30 \\ 8 b + 5 c = 11 \\ - 3 a + 10 c = 73 \end{array}$

Short Answer

Expert verified

The solution is $a = - 1, b = - 3, c = 7 .$

Step by step solution

Step-1 –Using elimination to obtain two equations in two variables

Given equations are

$\begin{array}{l} 9 a + 7 b = - 30 \\ 8 b + 5 c = 11 \\ - 3 a + 10 c = 73 \end{array}$

Multiplying third equation by $3$ and adding to the first equation, we get

$\begin{array}{l} 7 b + 30 c = - 30 + 219 \\ 7 b + 30 c = 189 \end{array}$

Step-2 –Solving the system of two equations in two variables

System of equations in two variables are

$\begin{array}{l} 8 b + 5 c = 11 \\ 7 b + 30 c = 189 \end{array}$

Multiplying the first equation by $6$ and subtracting with second equation, we get

$\begin{array}{l} 48 b - 7 b = 66 - 189 \\ 41 b = - 123 \\ b = - 3 \end{array}$

Putting the value of $b$ in equation $8 b + 5 c = 11$ we get

$\begin{array}{l} 8 (- 3) + 5 c = 11 \\ - 24 + 5 c = 11 \\ 5 c = 11 + 24 \\ 5 c = 35 \\ c = 7 \end{array}$

Step-3 –Evaluating the value of a by using the values of bandc

From the equation $9 a + 7 b = - 30$ we get

$\begin{array}{l} 9 a + 7 (- 3) = - 30 \\ 9 a - 21 = - 30 \\ 9 a = - 30 + 21 \\ 9 a = - 9 \\ a = - 1 \end{array}$

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.
$\begin{array}{l} 9 a + 7 b = - 30 \\ 8 b + 5 c = 11 \\ - 3 a + 10 c = 73 \end{array}$

Short Answer

Step by step solution

Step-1 –Using elimination to obtain two equations in two variables

Step-2 –Solving the system of two equations in two variables

Step-3 –Evaluating the value of a by using the values of bandc

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Decision Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations.9a+7b=−308b+5c=11−3a+10c=73

Short Answer

Step by step solution

Step-1 –Using elimination to obtain two equations in two variables

Step-2 –Solving the system of two equations in two variables

Step-3 –Evaluating the value of a by using the values of bandc

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Decision Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{array}{l} 9 a + 7 b = - 30 \\ 8 b + 5 c = 11 \\ - 3 a + 10 c = 73 \end{array}$