Explanation Given Information: The system of equations is 5 x + 7 = 8 y , 3 x = 8 y − 4 . Formula used: The elimination method is used to solve a system of equations and it allows the elimination of a variable. Step 1: Multiply the equations by a certain number first if needed. Step 2: Solve the equations for one variable by the addition principle. Step 3: Substitute the value of the variable obtained in step 2 in any of the provided equations to compute the value of the second variable. Calculation: Consider the system of equations, 5 x + 7 = 8 y , 3 x = 8 y − 4 Collect all the like terms on one side and label the equations as follows: 5 x − 8 y = − 7 …… ( 1 ) 3 x − 8 y = − 4 …… ( 2 ) Multiply the equation ( 2 ) by − 1 as follows: − 3 x + 8 y = 4 …… ( 3 ) Add equation ( 1 ) and ( 3 ) as follows: 5 x − 8 y = − 7 − 3 x + 8 y = 4 _ 2 x + 0 = − 3 Solve for x as follows: 2 x = − 3 x = − 3 2 Now substitute x = − 3 2 in equation ( 1 ) and solve for y as follows: 5 x − 8 y = − 7 5 ( − 3 2 ) − 8 y = − 7 − 15 2 − 8 y = − 7 − 8 y = 1 2 Solve further as follows: − 8 y = 1 2 y = 1 2 ⋅ − 1 8 = − 1 16 The solution of the provided system of equation is ( − 3 2 , − 1 16 )

16th Edition

ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 14.6, Problem 27ES

To determine

To calculate: The solution of the system of equations 5x+7=8y,3x=8y−4.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.6, Problem 26ES

Chapter 14.6, Problem 28ES

Students have asked these similar questions

Answer questions 8.1.10, 8.1.11and 8.1.12 respectively

7.2.10 Researchers in the Hopkins Forest also count the number of maple trees (genus acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard deviation of 23.65 trees. a. If we took the mean of a sample of eight plots, what would be the standard error of the mean? b. Using the central limit theorem, what is the probability that the mean of the eight would be within 1 standard error of the mean? c. Why might you think that the probability that you calculated in (b) might not be very accurate? 2. A normal population has mean 100 and variance 25. How large must the random sample be if you want the standard error of the sample average to be 1.5?

Answer questions 7.3.10 and 7.3.12 respectively 7.3.12. Suppose that two independent random samples (of size n1 and n2) from two normal distributions are available. Explain how you would estimate the standard error of the difference in sample means X1 − X2 with the bootstrap method.

Chapter 14 Solutions

DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<

Ch. 14.1 - Prob. 1SR Ch. 14.1 - Prob. 2SR Ch. 14.1 - Prob. 1DE Ch. 14.1 - Prob. 2DE Ch. 14.1 - Prob. 3DE Ch. 14.1 - Prob. 4DE Ch. 14.1 - Prob. 5DE Ch. 14.1 - Prob. 6DE Ch. 14.1 - Prob. 7DE Ch. 14.1 - Prob. 8DE

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The solution of the system of equations 5 x + 7 = 8 y , 3 x = 8 y − 4 .

Solution Summary: The author explains the elimination method used to solve a system of equations.

Concept explainers

Videos

To calculate: The solution of the system of equations 5x+7=8y,3x=8y−4.

Want to see the full answer?

Chapter 14 Solutions