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Systems of Linear Equations and Inequalities

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I am at a total loss on these. Any assistance you could give me would be greatly appreciated. I have a total of 9 problems. Thanks a lot!!

The start-up cost for producing widgets is $449, and each widget costs $91 to produce. What is the equation for this situation? Use X for # widgets produced and Y for cost.
a. none of the following
b. X = 449Y + 91
c. 91X + 449 = Y
d. Y = 449X + 91
e. X + Y = 449 + 91

A plumber charges $315 for 3 hrs works, and $635 for 7 hrs work. How much will he charge for 6 hrs work?
a. impossible to tell from info given
b. less than $500
c. at least $500 but less than $550
d. at least $550 but less than $600
e. at least $600

What is the slope of a line that passes thru the points (2, 5) and (-2, 6)?
a. less than -.1
b. at least -.1 but less than 0
c. at least 0 but less than +.1
d. at least +.1 but less than +.3
e. at least +.3

What is the slope of a horizontal line?
a. impossible to tell from info given
b. none of the following
c. 0
d. it doesn't exist
e. infinite

Why do we call the slope of a vertical line "undefined?"
a. impossible to tell from info given
b. because all Y's are the same, so Y2-Y1 = 0
c. because all X's are the same, so X2-X1 = 0
d. because the slope is parallel to the X-axis
e. because the slope is perpendicular to the Y-axis

The graph of a system of equations shows parallel lines. What is the solution to the system?
a. impossible to tell from info given
b. none of the following
c. the system has infinitely many solutions
d. the system is inconsistent
e. the system is dependent

Solve the following system of equations: 5X + 8Y = 1 and 3X - Y = -8
a. impossible to tell from info given or none of the following
b. (2, 3)
c. (-2, 3)
d. (3, 2)
e. (3, -2)

Which of the following is a solution to 4X - 2Y <= 9?
a. impossible to tell from info given or none of the following
b. all of the following
c. (0, 0)
d. (8, 12)
e. (1, -2)

Write in mathematical symbols: the proportion is a majority
a. impossible to tell from info given
b. none of the following
c. p = ½
d. p >= ½
e. p < 1/2

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Solution Summary

Systems of linear equations and inequalities are provided.

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The start-up cost for producing widgets is $449, and each widget costs $91 to produce. What is the equation for this situation? Use X for # widgets produced and Y for cost.
a. none of the following
b. X = 449Y + 91
c. 91X + 449 = Y
d. Y = 449X + 91
e. X + Y = 449 + 91

The answer is C: 91X + 449 = Y

A plumber charges $315 for 3 hrs works, and $635 for 7 hrs work. How much will he charge for 6 hrs work?
a. impossible to tell from info given
b. less than $500
c. at least $500 but less than $550
d. at least $550 but less than $600
e. at least $600

The answer is a) impossible to tell from info ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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