Chapter 11: Q. 47 (page 756)

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} 6 x + 5 y = 13 \\ 2 x + 2 y = 5 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations $\{\begin{cases} 6 x + 5 y = 13 \\ 2 x + 2 y = 5 \end{cases}$ is, $x = \frac{1}{2}, y = 2$ .

Step by step solution

Step 1. Given information

$\{\begin{cases} 6 x + 5 y = 13 \\ 2 x + 2 y = 5 \end{cases}$

The inverse found in problem $33$ is, $[\begin{matrix} 1 & - \frac{5}{2} \\ - 1 & 3 \end{matrix}]$ .

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

From the given information, $B = [\begin{matrix} 13 \\ 5 \end{matrix}]$ .

Substitute the known values in the formula.

$[\begin{matrix} x \\ y \end{matrix}] = X X = [\begin{matrix} 1 & - \frac{5}{2} \\ - 1 & 3 \end{matrix}] [\begin{matrix} 13 \\ 5 \end{matrix}] = [\begin{matrix} 1 (13) - \frac{5}{2} (5) \\ - 1 (13) + 3 (5) \end{matrix}] = [\begin{matrix} 13 - \frac{25}{2} \\ - 13 + 15 \end{matrix}] = [\begin{matrix} \frac{1}{2} \\ 2 \end{matrix}]$

So, the solution is, in ordered pairs $(\frac{1}{2}, 2)$ or $x = \frac{1}{2}, y = 2$ .

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In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} 6 x + 5 y = 13 \\ 2 x + 2 y = 5 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

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

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In Problems 41-60, use the inverses found in Problems 31-40to solve each system of equations.6x+5y=132x+2y=5

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

Decision Maths

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} 6 x + 5 y = 13 \\ 2 x + 2 y = 5 \end{cases}$