Chapter 11: Q. 46 (page 756)

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} - 4 x + y = 0 \\ 6 x - 2 y = 14 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations $\{\begin{cases} - 4 x + y = 0 \\ 6 x - 2 y = 14 \end{cases}$ is, $x = - 7, y = - 28$ .

Step by step solution

Step 1. Given information

$\{\begin{cases} - 4 x + y = 0 \\ 6 x - 2 y = 14 \end{cases}$

The inverse found in problem $34$ is, $[\begin{matrix} - 1 & \frac{- 1}{2} \\ - 3 & - 2 \end{matrix}]$ .

Step 2. We know that, X=A-1.B

From the given information, $B = [\begin{matrix} 0 \\ 14 \end{matrix}]$ .

Substitute the known values in the formula.

$[\begin{matrix} x \\ y \end{matrix}] = X X = [\begin{matrix} - 1 & \frac{- 1}{2} \\ - 3 & - 2 \end{matrix}] [\begin{matrix} 0 \\ 14 \end{matrix}] = [\begin{matrix} - 1 (0) - \frac{1}{2} (14) \\ - 3 (0) - 2 (14) \end{matrix}] = [\begin{matrix} 0 - 7 \\ 0 - 28 \end{matrix}] = [\begin{matrix} - 7 \\ - 28 \end{matrix}]$

So, the solution is, in ordered pairs $(- 7, - 28)$ or $x = - 7, y = - 28$ .

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.

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} - 4 x + y = 0 \\ 6 x - 2 y = 14 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. We know that, X=A-1.B

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 41-60, use the inverses found in Problems 31-40to solve each system of equations.-4x+y=06x-2y=14

Short Answer

Step by step solution

Step 1. Given information

Step 2. We know that, X=A-1.B

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} - 4 x + y = 0 \\ 6 x - 2 y = 14 \end{cases}$