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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. 75 (page 757)

Algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x + 3 y = 11 \\ 5 x + 7 y = 24 \end{cases}$

Short Answer

Expert verified

The values of x and y are $- 5 & 7$

Step by step solution

01

Step 1.Given information

Given equation are $2 x + 3 y = 11 & 5 x + 7 y = 24$

02

Step 2.Conversion of equations

Matrix form $[\begin{matrix} 2 & 3 \\ 5 & 7 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 11 \\ 24 \end{matrix}]$

03

Step 3.Reduction of matrix

Reducing the matrix

{R_{1} 鈫� \frac{R_{1}}{2}} [\begin{matrix} 1 & 1.5 \\ 5 & 7 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5.5 \\ 24 \end{matrix}] {R_{2} 鈫� R_{2} - 5 R_{1}} [\begin{matrix} 1 & 1.5 \\ 0 & - 0.5 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5.5 \\ - 3.5 \end{matrix}] {R_{2} 鈫� - 2 R_{2}} [\begin{matrix} 1 & 1.5 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5.5 \\ 7 \end{matrix}] {R_{1} 鈫� R_{1} - 5 R_{2}} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} - 5 \\ 7 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} - 5 \\ 7 \end{matrix}]

04

Step 4.The solution

The values of x and y are $- 5 & 7$

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Most popular questions from this chapter

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$x y = 4; x^{2} + y^{2} = 8$

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{array}{r} x + 2 y = - 7 \\ x + y = - 3 \end{array}$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\{\begin{cases} y = x^{2} + 1 \\ y = x + 1 \end{cases}$

An area of $52 f e e t^{2}$ is to be enclosed by two squares whose sides are in the ratio of $2 : 3$ . Find the sides of the squares.

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

$x^{2} + y^{2} = 4; y^{2} - x = 4$

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