Question

1.

A student is trying to solve the system of two equations given below:

Equation P: a + b = 6
Equation Q: 4a + 2b = 19

Which of the following steps can be used to eliminate the a term? (4 points)



–1(4a + 2b = 19)
–4(4a + 2b = 19)
–4(a + b = 6)
4(a + b = 6)
2.
Jordan wants to solve the following system using the elimination method:

2x + 3y = 10
x + y = 7

What number should the equation x + y = 7 be multiplied by to eliminate y? (4 points)



–2
2
–3
3
3.
Jemma wants to solve the following system using the elimination method:

y = x – 6
y = 6x – 19

What number should the equation y = x – 6 be multiplied by to eliminate x? (4 points)



1
2
4
–6
4.
Which of the following ordered pairs represents the solution to the system given below?

x – 4y = 7
5x + 9y = 6 (4 points)



(3, –1)
(3, 1)
(1, –3)
(–1, –3)
5.
The work of a student to solve a set of equations is shown below:

Equation 1: x + 2y = 10
Equation 2: 2x + 5y = 15

Step 1: –2(x + 2y) = –2(10)
2x + 5y = 15

Step 2: –2x – 4y = –10
2x + 5y = 15

Step 3: 1y = 5

Step 4: x + 2(1) = 10

Step 5: x = 8


In which step did the student first make an error? (4 points)



Step 1
Step 2
Step 3
Step 4

Answer 1

1. Choose C. When you want to eliminate a, the equation has to have opposite values that cancel out. If you already have 4a, you want to get -4a, which is -4*a shown in the third option.

2. -3. Since we already have 3 y, we want -3 y so it can cancel out since 3-3=0.

3. -6. We have 6x already so we want -6x to cancel out since 6-6=0.

4.
-5x+20y=-35
5x+9y=6
29y=-29
y=-1

5x+9(-1)=6
5x-9=6
5x=15
x=3

Final answer: (3,-1)

5. The error is in step 2 since they forgot to multiply -2(10)