A system of equations | Algebra homework help
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<object:standard:macc.912.a–rei.3.5>A system of equations is shown below:
x + 3y = 5 (equation 1)
7x – 8y = 6 (equation 2)
A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?
Question 2
(05.02)<object:standard:macc.912.a–rei.3.6>
Solve the following system of equations:
3x – 2y = 6
6x – 4y = 12
Question 3
(05.01)<object:standard:macc.912.a–rei.3.6>
Which graph below shows a system of equations with infinitely many solutions?
Question 4
(05.02)<object:standard:macc.912.a–rei.3.6>
A system of equations is shown below:
x + y = 3
2x – y = 6
The x-coordinate of the solution to this system of equations is _____.
Numerical Answers Expected!
Answer for Blank 1:
Question 6
(05.06)<object:standard:macc.912.a–ced.1.3>
Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?
Question 7
(05.02)<object:standard:macc.912.a–rei.3.5>
Two systems of equations are shown below:
System A |
System B |
2x + y = 5 |
-10x + 19y = -1 |
-4x + 6y = -2 |
-4x + 6y = -2 |
Which of the following statements is correct about the two systems of equations?
Question 8
(05.06)<object:standard:macc.912.a–rei.4.12>
A system of linear inequalities is shown below:
y – x > 0
x + 1 < 0
Which of the following graphs best represents the solution set to this system of linear inequalities?
Question 9
(05.02)<object:standard:macc.912.a–rei.3.6>
The total price of a shirt and a cap is $11. If the price of the shirt was doubled and the price of the cap was 3 times its original price, the total price of a shirt and a cap would be $25. What is the price of a shirt and a cap?
Question 10
(05.05)<object:standard:macc.912.a–rei.4.12>
Select the inequality that corresponds to the given graph.
Question 11
(05.03)<object:standard:macc.912.a–rei.4.10>
The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
Question 12
(05.03)<object:standard:macc.912.a–rei.4.11>
The tables below show the values of f(x) and g(x) for different values of x:
f(x) = 2(3)x
g(x) = 3x + 9
x | g(x) |
-2 | 9.11 |
-1 | 9.33 |
0 | 10 |
1 | 12 |
2 | 18 |
Based on the tables, what is the solution to the equation 2(3)x = 3x + 9?
Question 13
(05.03)<object:standard:macc.912.a–rei.4.11>
An equation is shown below:
What is the solution to the equation?
Question 14
(05.02)<object:standard:macc.912.a–ced.1.3>
Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya had bought 2 burgers and 1 sandwich, she would have been left with $11.
A student concluded that the price of each burger is $5 and the price of each sandwich is $6. Which statement best justifies whether the student’s conclusion is correct or incorrect?
Question 15
(05.06)<object:standard:macc.912.a–rei.4.12>
Look at the graph below:
Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ –1?
Question 16
(05.05)<object:standard:macc.912.a–rei.4.12>
A graph is shown below:
Which of the following inequalities is best represented by this graph?
Question 17
(05.01)<object:standard:macc.912.a–rei.3.6>
The graph plots four equations, A, B, C, and D:
Which pair of equations has (0, 8) as its solution?
Question 18
(05.03)<object:standard:macc.912.a–rei.4.11>
The graph below shows two functions:
Based on the graph, what are the approximate solutions to the equation –2x + 8 = (0.25)x?
Question 19
(05.05)<object:standard:macc.912.a–rei.4.12>
Greg made 4 chairs and 3 tables. Greg only has enough plywood to make at most 15 chairs or tables total. Let x represent the number of more chairs and y represent the number of more tables that Greg can make. Which of the following graphs best represents the relationship between x and y?
Question 20
(05.02)<object:standard:macc.912.a–rei.3.6>
For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you substitute into the second equation?
-x – 2y = -4
3x + y = 12
Question 21
(05.05)<object:standard:macc.912.a–rei.4.12>
Sally has only nickels and dimes in her money box. She knows that she has less than $20 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y?
Question 22
(05.03)<object:standard:macc.912.a–rei.4.10>
Which of the following statements best describes the graph of –5x + 2y = 1?
Question 23
(05.01)<object:standard:macc.912.a–rei.3.6>
A pair of linear equations is shown below:
y = –x + 1
y = 2x + 4
Which of the following statements best explains the steps to solve the pair of equations graphically?