/*! 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 19 \(2 x+y=5 ; \quad(3,-1)\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 19

\(2 x+y=5 ; \quad(3,-1)\)

Short Answer

Expert verified
(3, -1) lies on the line.

Step by step solution

01

- Understanding the Exercise

Determine if the point (3, -1) lies on the line given by the equation: \(2x + y = 5\). This involves substituting the coordinates of the point into the equation and checking if the equation holds true.
02

- Substitute the Coordinates

Substitute \(x = 3\) and \(y = -1\) into the equation: \(2(3) + (-1) = 5\).
03

- Simplify and Verify

Calculate the left-hand side: \(2(3) + (-1) = 6 - 1 = 5\). Since the result equals the right-hand side (5), the point (3, -1) satisfies the equation.
04

- Conclusion

Since the left-hand side equals the right-hand side after substituting the coordinates, the point (3, -1) does lie on the line.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear equations
Linear equations are equations of the first degree, which means they have no exponents higher than one. They typically follow the form:
  • y = mx + b
  • Ax + By = C
Here, A, B, and C are constants, and x and y are variables. Linear equations graph as straight lines on the coordinate plane. They are foundational in algebra because they represent relationships with a constant rate of change. The exercise equation,
  • 2x + y = 5,
fits this form. Understanding linear equations helps in various fields such as physics, economics, and engineering.
coordinate substitution
In mathematics, coordinate substitution is a method where we insert known values of coordinates into an equation to verify or solve for the unknowns. When given a point and a line equation, substitute the x and y coordinates of the point into the equation to see if it satisfies the line equation. For instance, in our problem, we substitute
  • x = 3 and y = -1
into the equation
  • 2x + y = 5.
This substitution transforms the equation into numerical values that are easier to verify. Coordinate substitution forms the basis of many algebraic verification techniques, making it a crucial skill for students.
verification process
The verification process involves checking if a certain condition or statement is true. In our exercise, we need to verify if the point (3, -1) lies on the line given by
  • 2x + y = 5.
We start by substituting the x and y values with 3 and -1 respectively:
  • 2(3) + (-1).
Simplifying this, we get:
  • 6 - 1 = 5.
Since the left-hand side equals the right-hand side (5), the point satisfies the equation. This confirms that the point (3, -1) lies on the line. Verification confirms the accuracy of initial assumptions or hypotheses in both mathematical problems and real-world scenarios.

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

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 2 x=4 y $$

Write an equation of the line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form. (8,5) and (9,6)

Graph each linear equation. $$ y=4 x $$

Find the \(x\) - and \(y\) -intercepts for the graph of each equation. $$ y=3 x+6 $$

The height \(y\) (in centimeters) of a woman can be approximated by the linear equation $$ y=3.9 x+73.5 $$ where \(x\) is the length of her radius bone in centimeters. (a) Use the equation to approximate the heights of women with radius bones of lengths \(20 \mathrm{~cm}, 22 \mathrm{~cm},\) and \(26 \mathrm{~cm}\). (b) Write the information from part (a) as three ordered pairs. (c) Graph the equation for \(x \geq 20\), using the data from part (b). (d) Use the graph to estimate the length of the radius bone in a woman who is \(167 \mathrm{~cm}\) tall. Then use the equation to find the length of the radius bone to the nearest centimeter.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

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.