/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Determine whether the given orde... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 4

Determine whether the given ordered pair is a solution of the system. \((8,5)\) \(\left\\{\begin{array}{l}5 x-4 y=20 \\ 3 y=2 x+1\end{array}\right.\)

Short Answer

Expert verified
No, the ordered pair \((8,5)\) is not a solution to the system of equations.

Step by step solution

01

Substitute ordered pair values in first equation

The first equation is \(5x - 4y = 20\). Substitute \(x=8\) and \(y=5\) into the equation. This gives \(5*8 - 4*5\). The left hand side simplifies to 40 - 20 = 20, which equals the right hand side. Thus, the ordered pair holds true for the first equation.
02

Substitute ordered pair values in second equation

The second equation is \(3y = 2x + 1\). Substitute \(x=8\) and \(y=5\) into the equation. This gives \(3*5 = 2*8 + 1\). The left hand side simplifies to 15, and the right hand side simplifies to 17. Thus, the ordered pair does not hold true for the second equation. If the ordered pair doesn't satisfy ALL the equations in the system, it is not a solution to the system.
03

Conclusion

Since both equations should be true for the ordered pair to be a solution to the system, and it does not hold for the second equation, we can conclude that the ordered pair \((8,5)\) is not a solution to the system of equations.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Graph each linear inequality. \(x \geq 0\)

Graph each linear inequality. \(2 y-x>4\)

a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(y=-x^{2}+4 x-3\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x \geq 4 \\ y \leq 2\end{array}\right.\)

The data can be modeled by $$ f(x)=782 x+6564 \text { and } g(x)=6875 e^{0.077 x} \text {, } $$ in which \(f(x)\) and \(g(x)\) represent the average cost of a family health insurance plan \(x\) years after 2000. Use these functions to solve Exercises 33-34. Where necessary, round answers to the nearest whole dollar. a. According to the linear model, what was the average cost of a family health insurance plan in 2008 ? b. According to the exponential model, what was the average cost of a family health insurance plan in 2008 ? c. Which function is a better model for the data in 2008 ?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.