/*! 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 31 Solve each system by the additio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 31

Solve each system by the addition method. Be sure to check all proposed solutions. \(\left\\{\begin{array}{l}4 x+3 y=15 \\ 2 x-5 y=1\end{array}\right.\)

Short Answer

Expert verified
The solution to the system of equations is \(x = 3\) and \(y = 1\).

Step by step solution

01

Identify the Equations

Identify the two equations given in the system: Eq1: \(4x + 3y = 15\), Eq2: \(2x - 5y = 1\)
02

Manipulate the Equations

Manipulate the equations to get them to a point where they can be added to eliminate one of the variables. Multiply Eq1 by 5 and Eq2 by 3 to be able to eliminate \(y\). This gives: New Eq1: \(20x + 15y = 75\), New Eq2: \(6x - 15y = 3\).
03

Add the Equations

Add the newly computed Eq1 and Eq2. This eliminates the \(y\) variable and leaves us with an equation in \(x\) only: \(26x = 78\).
04

Solve for \(x\)

Divide both sides of the equation by 26 to solve for \(x\): \(x = 3\).
05

Substitute the Value of \(x\)

Substitute the value of \(x\) into one of the original equations (Eq2) to find the value of \(y\): \(2*3 - 5y = 1\), which gives \(6 - 5y = 1\). Now solve for \(y\): \(y = 1\).
06

Verify the Solution

Substitute the values \(x = 3\) and \(y = 1\) into both original equations to verify if they hold true. In Eq1, that gives \(4*3 + 3*1 = 12 + 3 = 15\). In Eq2, we get \(2*3 - 5*1 = 6 - 5 =1\). Both equations hold true, confirming that the solution is correct.

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. \(y>\frac{1}{4} x\)

In Exercises 23-38, graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}3 x+6 y \leq 6 \\ 2 x+y \leq 8\end{array}\right.\)

Make Sense? In Exercises 58-61, determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing a linear inequality, I should always use \((0,0)\) as a test point because it's easy to perform the calculations when 0 is substituted for each variable.

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & 4 \\ \hline 1 & 1 \\ \hline 2 & 0 \\ \hline 3 & 1 \\ \hline 4 & 4 \\ \hline \end{array} $$

Write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the \(x\)-variable and the \(y\)-variable is at most 3 . The \(y\)-variable added to the product of 4 and the \(x\)-variable does not exceed \(6 .\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

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.