coolgirlkx
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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

Verified Answer :

naǫ

Question 1:
\(n = 3m + 6 \\ n - 2m = 2 \\ \\ \hbox{substitute 3m+6 for n in the second equation:} \\ 3m+6-2m=2 \\ m+6=2 \ \ \ \ \ \ \ \ \ \ \ \ \ |-6 \\ m=-4 \\ \\ n=3m+6=3 \times (-4)+6=-12+6=-6 \\ \\ (m,n)=(-4,-6)\)

The answer is (-4,-6).

Question 2:
\(2(y + 6) = 4y \\ 2 \times y + 2 \times 6=4y \\ 2y+12=4y \ \ \ \ |-2y \\ 12=2y \ \ \ \ \ \ \ \ \ \ \ |\div 2 \\ y=6\)

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:

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

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

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

Step-by-step 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.

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