Question

Question 1 (5 points)

(03.06A LC)
How many solutions does the equation 4p + 7 = 3 + 4 + 4p have? (5 points)

a
One

b
Two

c
Infinitely many

d
None

Question 2 (5 points)
(03.06A HC)
The work of a student to solve the equation 2(3x − 4) = 8 + 2x + 4 is shown below:

Step 1: 2(3x − 4) = 8 + 2x + 4
Step 2: 5x − 6 = 12 + 2x
Step 3: 5x − 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6

In which step did the student first make an error and what is the correct step? (5 points)

a
Step 2; 6x − 6 = 2(6 + x + 2)

b
Step 2; 6x − 8 = 12 + 2x

c
Step 3; 5x − 2x = 12 − 6

d
Step 3; 5x + 2x = 12 + 6

Question 3 (5 points)
(03.06A LC)

Which statement is true about the equation fraction 3 over 4 z − fraction 1 over 4 z + 3 = fraction 2 over 4 z + 5? (5 points)

a
It has no solution.

b
It has one solution.

c
It has two solutions.

d
It has infinitely many solutions.

Question 4 (5 points)
(03.06A MC)
What is the solution to the equation 1.6m − 4.8 = −1.6m? (5 points)

a
m = 0.5

b
m = 0.7

c
m = 1.5

d
m = 3

Question 5 (5 points)
(03.07A MC)
Two lines, C and D, are represented by the equations given below:

Line C: y = x + 14
Line D: y = 3x + 2

Which of the following shows the solution to the system of equations and explains why? (5 points)

a
(6, 20), because both lines pass through this point

b
(6, 20), because the point does not lie on any axis

c
(3, 11), because one of the lines passes through this point

d
(3, 11), because the point lies between the two axes

Question 6 (5 points)
(03.07A LC)

The coordinate grid shows the graph of four equations:

A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.

Which set of equations has (3, 1) as its solution? (5 points)

a
A and B

b
C and D

c
B and D

d
A and D

Question 7 (5 points)
(03.07A MC)
Two equations are given below:

a − 3b = 16
a = b − 2

What is the solution to the set of equations in the form (a, b)? (5 points)

a
(−2, −6)

b
(−7, −9)

c
(−11, −9)

d
(−12, −10)

Question 8 (5 points)
(03.07A LC)
Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's age (p) and Winnie's age (w):

p = w + 2
p = 7w − 16

Which is a possible correct method to find Peter's and Winnie's ages? (5 points)

a
Solve w + 2 = 7w − 16 to find the value of w.

b
Solve p + 2 = 7p − 16 to find the value of p.

c
Write the points where the graphs of the equations intersect the x axis.

d
Write the points where the graphs of the equations intersect the y axis.

Question 9 (10 points)
(03.07A MC)
A pair of equations is shown below:

y = 7x − 8
y = 5x − 2

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)

Answer 1

• 1. C, 2. B, 3. A, 4. C, 5. A, 6. - 7. C, 8. A, 9. (3, 13)

Explanation:

Question 1

• 4p + 7 = 3 + 4 + 4p
• 4p + 7 = 4p + 7

Both sides are equal, so any value of p makes it right. It means there are infinitely many solutions

Question 2

2(3x − 4) = 8 + 2x + 4

Step 2 was wrong, it should be 6x - 8 = 12 + 2x

Question 3

• 3/(4z) - 1/(4z) + 3 = 2/(4z) + 5
• 2/(4z) + 3 = 2/(4z) + 5
• 3 = 5

It ends up with false equation, so no solution.

Question 4

• 1.6m − 4.8 = −1.6m
• 1.6m + 1.6m = 4.8
• 3.2m = 4.8
• m = 4.8/3.2
• m = 1.5

Question 5

Line C: y = x + 14

Line D: y = 3x + 2

• x+ 14 = 3x + 2
• 3x - x = 14 - 2
• 2x = 12
• x = 6

• y = 6 + 14 = 20

Solution is (6, 20), this is the intersection of lines

Question 6

• It should have a graph attached, so ignored

Question 7

• a − 3b = 16
• a = b − 2

• b - 2 - 3b = 16 ⇒ -2b = 18 ⇒ b = - 9

• a = - 9 - 2 = - 11

Solution is (a, b) = (- 11, - 9)

Question 8

• p = w + 2
• p = 7w − 16

Easy method is substitution: w + 2 = 7w - 16

Question 8

• y = 7x − 8
• y = 5x − 2

Easy method is substitution:

• 7x - 8 = 5x - 2
• 7x - 5x = 8 - 2
• 2x = 6
• x = 3

• y = 7*3 - 8 = 21 - 8 = 13

• The point (3, 13) is the solution and it is the intersection of the lines.