Question

Question 1

A system of equations is shown below:
   n = 3m + 6
   n − 2m = 2



What is the solution, in the form (m, n), to the system of equations?

(−4, −6)
(−5, −9)
(2, 6)
(1, 8)

Question 2

The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below:

STEP1: 2(y + 6) = 4y
Step 2: 2y + 8 = 4y
Step 3: 2y = 8
Step 4: y = 4

Which of the following explains how to correct Step 2 and shows the correct value of y?

2 should be distributed as 2y + 12; y = 6
2 should be distributed as 2y + 12; y = 3
The equation should be y + 6 = 4y after division by 2; y = 2
The equation should be y + 6 = 4y after division by 2; y = 1


Question 3
The equation 3.3x − 6.6 = 2.7x can be transformed to form which of the following expressions?

6.0x = 6.6
0.6x = 6.6
6.0x = −6.6
0.6x = −6.6

Answer 1

Question 1:

`n = 3m + 6 \\ n - 2m = 2 \\ \\ \hbox{substitute 3m+6 for n in the second equation:} \\ 3m+6-2m=2 \\ m+6=2 \ \ \ \ \ \ \ \ \ \ \ \ \ |-6 \\ m=-4 \\ \\ n=3m+6=3 * (-4)+6=-12+6=-6 \\ \\ (m,n)=(-4,-6)`

The answer is (-4,-6).

Question 2:

`2(y + 6) = 4y \\ 2 * y + 2 * 6=4y \\ 2y+12=4y \ \ \ \ |-2y \\ 12=2y \ \ \ \ \ \ \ \ \ \ \ |/ 2 \\ y=6`

The answer is: 2 should be distributed as 2y + 12; y = 6.

Question 3:

`3.3x-6.6=2.7x \ \ \ \ |-2.7x \\ 0.6x-6.6=0 \ \ \ \ \ \ \ \ |+6.6 \\ 0.6x=6.6`

The answer is 0.6x=6.6.

Answer 2

Part 1: The solution is (-4,-6)

Part 2: 2 should be distributed as 2y + 12; y = 6

Part 3:
`\text{The solution is }0.6x=6.6`

Explanation:

Part 1: Given the system of equations

`n - 3m = 6` → (1)

`n - 2m = 2` → (2)

Solving above two equations

Subtract 2 from 1, we get

`n-3m-(n-2m)=6-2`

`2m-3m=4`

`m=-4`

(1) ⇒
`n=3(-4)+6=-12+6=-6`

The solution is (-4,-6)

Option 1 is correct.

Part 2: The incorrect work of a student to solve an equation 2(y + 6) = 4y

we have to choose the correct step to solve value of y

Equation: 2(y + 6) = 4y

By distributive property

2y+12=4y

2y=12 ⇒ y=6

Hence, 2 should be distributed as 2y + 12; y = 6

∴ Option 1 is correct.

Part 3: Given the equation 3.3x − 6.6 = 2.7x

we have to solve

3.3x − 6.6 = 2.7x

Subtracting 2.7x both sides

`3.3x-2.7x=6.6`

`0.6x=6.6`

Option 2 is correct.