Chapter 11: Q. 41 (page 756)

In Problems $41 - 60$ , use the inverses found in Problems 31–40 to solve each system of equations.
$\{\begin{cases} 2 x + y = 8 \\ x + y = 5 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations $\{\begin{cases} 2 x + y = 8 \\ x + y = 5 \end{cases}$ is, $(3, 2)$ .

Step by step solution

Step 1. Given information

$\{\begin{cases} 2 x + y = 8 \\ x + y = 5 \end{cases}$

The inverse found in problem $31$ is, $[\begin{matrix} 1 & - 1 \\ - 1 & 2 \end{matrix}]$

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

From the given information, $B = [\begin{matrix} 8 \\ 5 \end{matrix}]$

Substitute the known values in the formula.

role="math" localid="1647416830279" $X = [\begin{matrix} 1 & - 1 \\ - 1 & 2 \end{matrix}] [\begin{matrix} 8 \\ 5 \end{matrix}] = [\begin{matrix} (1 \times 8) - 1 (5) \\ (- 1 \times 8) + 10 \end{matrix}] = [\begin{matrix} 8 - 5 \\ - 8 + 10 \end{matrix}] = [\begin{matrix} 3 \\ 2 \end{matrix}]$

So, the obtained solution is, $x = 3, y = 2$ or using ordered pair $(3, 2)$ .

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In Problems $41 - 60$ , use the inverses found in Problems 31–40 to solve each system of equations.
$\{\begin{cases} 2 x + y = 8 \\ x + y = 5 \end{cases}$

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 31–40 to solve each system of equations.2x+y=8x+y=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

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems $41 - 60$ , use the inverses found in Problems 31–40 to solve each system of equations.
$\{\begin{cases} 2 x + y = 8 \\ x + y = 5 \end{cases}$