/*! 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 68 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 68

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

Short Answer

Expert verified
When \( y = 2 \), \( x \) is 0.

Step by step solution

01

Substitute the Given Value of y

We start by substituting the given value of \( y \) into the equation. We know \( y = 2 \), so we replace \( y \) in the equation: \[ 2x + 5(2) = 10 \] This simplifies to: \[ 2x + 10 = 10 \]
02

Simplify the Equation

Now simplify the equation by subtracting 10 from both sides. This will help us isolate the term with \( x \):\[ 2x + 10 - 10 = 10 - 10 \]Simplifying the left side gives:\[ 2x = 0 \]
03

Solve for x

Now, solve for \( x \) by dividing both sides of the equation by 2:\[ \frac{2x}{2} = \frac{0}{2} \]This simplifies to:\[ x = 0 \]

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
Solving equations is a fundamental skill in algebra. When solving an equation, our goal is to find the value of the variable that makes the equation true. In our example, the variable is \(x\).

Here's how it works step by step.
  • First, we substitute any known values into the equation. This helps in simplifying the equation and makes our task easier.
  • Next, we simplify the equation if possible. This could mean combining like terms or moving numbers to different sides of the equation.
  • Finally, we solve for the variable. This often involves performing inverse operations like addition, subtraction, multiplication, or division to isolate the variable.
These steps ensure a clear path to finding the correct value for the variable, which keeps us organized and on track.
Prealgebra
Prealgebra is the foundation of all algebra studies, and it introduces the basic concepts students need to tackle more advanced topics later.

Prealgebra involves:
  • Understanding numbers and how they work 鈥� integers, fractions, and decimals.
  • Learning how to manipulate numbers with basic operations like addition, subtraction, multiplication, and division.
  • Grasping the concept of variables and how they can stand in for unknown values in equations.
By mastering prealgebra, students gain the confidence to work with equations and expression setups, ensuring a smoother transition to more complex algebraic concepts. This foundation is essential for solving equations effectively.
Substitution Method
The substitution method is one of the key techniques used in algebra to solve equations, particularly when dealing with systems of equations. It involves replacing a variable with a value or another expression to simplify the problem.

Let鈥檚 break down the steps:
  • First, solve one of the equations for one of the variables if it isn't already isolated.
  • Then, substitute the expression (or value) into the other equation. This eliminates one variable, leaving an equation with a single variable.
  • Solve this new equation for the remaining variable.
  • Substitute back the found value to determine the other variable, if necessary.
This method is especially useful when one of the equations is already easy to solve for a variable. In our exercise, directly substituting the given value for \(y\) simplifies our work and leads us quickly to the solution, providing an efficient path to solve for \(x\).

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

The problems below review material we covered in Section 4.9 Graph each equation. $$x-y=3$$

The problems below review material we covered in Section 4.9 Graph each equation. $$x+y=3$$

Reduce to lowest terms. $$\frac{75}{100}$$

The problems below review material we covered in Section 4.9 Graph each equation. $$y=x+3$$

Find each of the following sums and differences. (Add or subtract.) $$5 \frac{35}{100}+2 \frac{3}{10}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

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.