/*! 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 67 Use the formula \(2 x+5 y=10\) t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 67

Use the formula \(2 x+5 y=10\) to find \(x\) if: $$y=0$$

Short Answer

Expert verified
If \( y = 0 \), then \( x = 5 \).

Step by step solution

01

Substitute the given value into the equation

We begin by substituting the value of \( y = 0 \) into the equation \( 2x + 5y = 10 \). This gives us \( 2x + 5(0) = 10 \).
02

Simplify the equation

Simplify the equation from Step 1. This means we have \( 2x + 0 = 10 \), which simplifies to \( 2x = 10 \).
03

Solve for \( x \)

To isolate \( x \), divide both sides of the equation \( 2x = 10 \) by 2. This results in \( x = \frac{10}{2} \), so \( x = 5 \).

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.

Step-by-step math solutions
Breaking down a math problem into clear, manageable steps can make solving equations much easier. Step-by-step solutions guide you through the process, one part at a time, helping to prevent mistakes and solidify your understanding.
To start, identify the problem and what is known and unknown. Take our example: the equation is \( 2x + 5y = 10 \) and we need to find \( x \) when \( y = 0 \).

Each step focuses on a single goal, such as substituting values or isolating a variable. With practice, these structured steps become second nature. Here's a tip: always check your work by substituting your solution back into the original equation to ensure it holds true.
Algebraic manipulation
Algebraic manipulation involves rearranging equations to either simplify them or to isolate a particular variable, using basic algebra skills. It's like solving a puzzle, where each move gets you closer to the solution.
Consider the equation \( 2x + 5y = 10 \). By substituting \( y = 0 \), you can simplify the expression. The equation becomes \( 2x + 0 = 10 \), which further simplifies to \( 2x = 10 \).
Here鈥檚 a quick checklist for algebraic manipulation:
  • Combine like terms.
  • Use inverse operations to move terms.
  • Multiply or divide every part of an equation equally.
Algebraic manipulation is a powerful tool, not just for solving equations, but for simplifying mathematical expressions and solving real-world problems mathematically.
Substitution method
The substitution method is a technique used to solve systems of equations or expressions by replacing variables with given values. This method simplifies problems by reducing the number of unknowns.
In our example, \( y \) is given as 0. By substituting \( y = 0 \) into the equation \( 2x + 5y = 10 \), the equation then reduces to \( 2x = 10 \).
After substitution, you often find that solving for the remaining variables becomes straightforward. Here鈥檚 how it works:
  • Identify the given variable value(s).
  • Substitute these into the original equation.
  • Simplify the equation to solve for the unknowns.
The substitution method helps break down complex equations, making them easier and quicker to solve, especially useful in finding specific solutions in algebraic problems.

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

How many hours does a person making \(\$ 6.78\) per hour have to work in order to earn \(\$ 257.64 ?\)

Use a calculator to show that \(\sqrt{2}+\sqrt{3}\) is not the same as \(\sqrt{5}.\)

Carry out cach of the following divisions only so far as needed to round the results to the nearest hundredth. $$4 . 4 \longdiv { 7 5 }$$

Carry out cach of the following divisions only so far as needed to round the results to the nearest hundredth. $$0.543 \div 2.1$$

Suppose a woman earns \(\$ 6.78\) an hour for the first 36 hours she works in a week and then \(\$ 10.17\) an hour in overtime pay for each additional hour she works in the same week. If she makes \(\$ 294.93\) in one week, how many hours did she work overtime?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.