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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 44 (page 756)

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
$\{\begin{cases} 3 x - y = 4 \\ - 2 x + y = 5 \end{cases}$

Short Answer

Expert verified

The solution of the system of equations $\{\begin{cases} 3 x - y = 4 \\ - 2 x + y = 5 \end{cases}$ is, $x = 9, y = 23$ .

Step by step solution

01

Step 1. Given information

$\{\begin{cases} 3 x - y = 4 \\ - 2 x + y = 5 \end{cases}$

The inverse found in problem $32$ is, $[\begin{matrix} 1 & 1 \\ 2 & 3 \end{matrix}]$ .

02

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

From the given information, $B = [\begin{matrix} 4 \\ 5 \end{matrix}]$ .

Substitute the known values in the formula.

$[\begin{matrix} x \\ y \end{matrix}] = X X = [\begin{matrix} 1 & 1 \\ 2 & 3 \end{matrix}] [\begin{matrix} 4 \\ 5 \end{matrix}] = [\begin{matrix} 1 (4) + 1 (5) \\ 2 (4) + 3 (5) \end{matrix}] = [\begin{matrix} 4 + 5 \\ 8 + 15 \end{matrix}] = [\begin{matrix} 9 \\ 23 \end{matrix}]$

So, the solution set is, in ordered pairs $(9, 23)$ or $x = 9, y = 23$ .

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