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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. 42 (page 756)

In Problems $41 - 60$ , use the inverses found in Problems $31 - 40$ to solve each system of equations.
role="math" localid="1647420018361" $\{\begin{cases} 3 x - y = 8 \\ - 2 x + y = 4 \end{cases}$

Short Answer

Expert verified

The solution for the system of equations $\{\begin{cases} 3 x - y = 8 \\ - 2 x + y = 4 \end{cases}$ is, $x = 12, y = 28$ .

Step by step solution

01

Step 1. Given information

$\{\begin{cases} 3 x - y = 8 \\ - 2 x + y = 4 \end{cases}$

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, $B = [\begin{matrix} 8 \\ 4 \end{matrix}]$ .

Substitute the known values in the formula.

role="math" localid="1647420384652" $[\begin{matrix} x \\ y \end{matrix}] = X X = [\begin{matrix} 1 & 1 \\ 2 & 3 \end{matrix}] [\begin{matrix} 8 \\ 4 \end{matrix}] = [\begin{matrix} (1 脳 8) + 1 (4) \\ (2 脳 8) + 3 (4) \end{matrix}] = [\begin{matrix} 8 + 4 \\ 16 + 12 \end{matrix}] = [\begin{matrix} 12 \\ 28 \end{matrix}]$

So, the solution is, in ordered pairs $(12, 28)$ or $x = 12, y = 28$ .

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Most popular questions from this chapter

In Problems, use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

$\frac{x^{4} + x^{3} - x + 2}{x^{2} - 2 x + 1}$

If a system of equations has no solution, it is said to be _______.

Solve each system of equations. If the system has no solution, say that it is inconsistent.

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

Graph each inequality by hand.

$x^{2} + y^{2} 鈮� 9$

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\{\begin{cases} 2 x + y 鈮� - 2 \\ 2 x + y 鈮� 2 \end{cases}$

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