/*! 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 133 Is \(x-4 y=14\) a true statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 133

Is \(x-4 y=14\) a true statement for \(x=12\) and \(y=1 ?\)

Short Answer

Expert verified
No, \(x - 4y = 14\) is not a true statement for \(x = 12\) and \(y = 1\)

Step by step solution

01

Substituting the value of x

Substitute the given value of x into the equation. This gives us: \(12 - 4y = 14\)
02

Substituting the value of y

Now, substitute the given value of y into the equation from Step 1. This gives us: \(12 - 4*1 = 12 - 4 = 8\)
03

Checking if the equation holds true

We now compare the outcome on the left side (8) against the value on the right side of the equation (14). Since 8 is not equal to 14, the equation does not hold true for the given values of x and y.

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.

Solving Equations
To determine if a given set of values satisfies an equation, such as \( x - 4y = 14 \), the process begins by solving the equation. Solving equations means finding the value of variables that make the equation true. In our original exercise, the task is to verify whether the equation holds true for given values. Consider the equation as a balance, where both sides have to equal each other. If they do, the equation is satisfied. In this case, you're not solving for \( x \) or \( y \) like we often do but checking if the balance holds with given values. This means substituting the values into the equation and solving any resulting arithmetic.
Substitution Method
One powerful method to test if values satisfy an equation is the substitution method. It involves replacing a variable within an equation with a specific value. This technique is incredibly useful when you're provided with certain values for the variables. In the original step-by-step solution:
  • First, the given value of \( x = 12 \) is substituted into the equation, which modifies \( x - 4y = 14 \) to \( 12 - 4y = 14 \).
  • Next, the given value of \( y = 1 \) is substituted into the equation, further simplifying it to \( 12 - 4 \times 1 = 12 - 4 = 8 \).
By performing this substitution, we aim to verify the truth of the equation given the values of \( x \) and \( y \). It's a straightforward step-by-step method that effectively shows if both sides of the equation can equal each other.
Checking Solutions
After performing the substitution method, the next step is to check if the values make both sides of the equation equal. This process is called checking solutions.
  • You calculate the expression on the left side after substitution, which in this case resulted in 8, and compare it to the right side of the original equation, which is 14.
  • If both sides are equal, then the equation holds true for the given values, confirming a solution. If they are not equal, as seen here (8 鈮� 14), then the provided values do not satisfy the equation.
Checking solutions helps you confirm whether or not the proposed solution is valid, essentially giving a final stamp of approval or disapproval on the values being tested.

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

Solve each inequality. $$5 x-4 \leq 4(x-1)$$

Solve for \(x: \frac{x}{2}+7=13-\frac{x}{4}\) (Section \(2.3,\) Example 4 )

A car can be rented from Basic Rental for \(\$ 60\) per week plus 50 cents for each mile driven. How many miles can you travel if you can spend at most \(\$ 600\) for the week?

Exercises \(91-93\) will help you prepare for the material covered in the next section. Simplify: \(13-3(x+2)\)

If the measures of two angles of a triangle are known, explain how to find the measure of the third angle.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.