/*! 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 6 If \(6 k-5 l=27\) and \(3 l-2 k=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 6

If \(6 k-5 l=27\) and \(3 l-2 k=-13\) and \(5 k-5 l=j,\) what is the value of \(j ?\)

Short Answer

Expert verified
The value of \(j\) is 42.5.

Step by step solution

01

Rewrite the equations

First, rewrite the equations in a consistent order, either \(kl\) or \(lk\). In this case, let's choose \(kl\): \[2k + 3l = -13\] \[6k - 5l = 27 \]
02

Multiply to eliminate one variable

Multiply the first equation by 2 and the second equation by 3 so that the coefficient of \(k\) is the same in both equations. This will give: \[4k + 6l = -26\] \[18k - 15l = 81 \]
03

Sum both equations

Next, add both equations to eliminate one variable, l in this case. This gives \(22k = 55\).
04

Solve for k

Solve for \(k\) to find \(k = 55 / 22 = 2.5\). This is the value of \(k\).
05

Substitute value of k into one of the original equations

Substitute \(k = 2.5\) into the first original equation \(2k + 3l = -13\). This gives \(5 + 3l = -13\), hence \(3l = -18\) and \(l = -18 / 3 = -6\). This is the value of \(l\).
06

Substitute values of k and l into the equation for j

Substitute \(k = 2.5\) and \(l = -6\) into the equation \(5k - 5l = j\) to find \(j\). This gives \(j = 5(2.5) + 5(6) = 12.5 + 30 = 42.5\).

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!

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

If \(3^{3} \times 9^{12}=3^{\mathrm{x}},\) what is the value of \(x ?\)

$$x^{2}+8 x=-7$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x & 0 \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal d. The relationship cannot be determined from the information given.

$$11 x+14 y=30 \text { and } 3 x+4 y=12$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x+y & (x+y)^{-2} \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \frac{2^{-4}}{4^{-2}} & \frac{\sqrt{64}}{-2^{3}} \end{array}$$ a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

If \(A=2 x-(y-2 c)\) and \(B=(2 x-y)-2 c,\) then \(A-B=\) a. \(-2 y\) b. \(-4 c\) c. \(-0\) d. \(-2 y\) e. \(-4 c\)
See all solutions

Recommended explanations on English Textbooks

5 Paragraph Essay

Read Explanation

Essay Writing Skills

Read Explanation

Linguistic Terms

Read Explanation

Language Analysis

Read Explanation

English Grammar Summary

Read Explanation

Global English

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.