A system of equations | Algebra homework help

<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 



Solve the following system of equations:
3x – 2y = 6
6x – 4y = 12




Question 3 



Which graph below shows a system of equations with infinitely many solutions?




Question 4 



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 



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 



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 



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 



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 



Select the inequality that corresponds to the given graph. 

graph with a y–intercept at 0 comma 1 and a second point at 4 comma 2. This is a dashed line with shading above the line




Question 11 



The graph of an equation is shown below:

line joining ordered pairs negative 3,2 and 1, negative 2

Based on the graph, which of the following represents a solution to the equation?




Question 12 



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 



An equation is shown below:

2 over 3 multiplied by x plus 8 over 3 equals 2 to the power of x

What is the solution to the equation?




Question 14 



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 



Look at the graph below:

First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3

Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ –1?




Question 16 



A graph is shown below:

solid line joining ordered pair 0, 0 and 8, 5 and the region below this line which lies in the first quadrant is shaded

Which of the following inequalities is best represented by this graph?




Question 17 



The graph plots four equations, A, B, C, and D:

Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7.

Which pair of equations has (0, 8) as its solution?




Question 18 



The graph below shows two functions:

function f of x is a straight line which joins the ordered pairs negative 3.5, 15 and 4, 0. Function g of x is a curved line which joins the ordered pairs negative 1.7, 11.5 and 4, 0

Based on the graph, what are the approximate solutions to the equation –2x + 8 = (0.25)x?




Question 19 



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 



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



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 



Which of the following statements best describes the graph of –5x + 2y = 1?




Question 23 



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?


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