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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. 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

01

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, $[\begin{matrix} 1 & - \frac{5}{2} \\ - 1 & 3 \end{matrix}]$ .

02

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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