Answer :
Question 1:
[tex]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)[/tex]
The answer is (-4,-6).
Question 2:
[tex]2(y + 6) = 4y \\ 2 \times y + 2 \times 6=4y \\ 2y+12=4y \ \ \ \ |-2y \\ 12=2y \ \ \ \ \ \ \ \ \ \ \ |\div 2 \\ y=6[/tex]
The answer is: 2 should be distributed as 2y + 12; y = 6.
Question 3:
[tex]3.3x-6.6=2.7x \ \ \ \ |-2.7x \\ 0.6x-6.6=0 \ \ \ \ \ \ \ \ |+6.6 \\ 0.6x=6.6[/tex]
The answer is 0.6x=6.6.
[tex]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)[/tex]
The answer is (-4,-6).
Question 2:
[tex]2(y + 6) = 4y \\ 2 \times y + 2 \times 6=4y \\ 2y+12=4y \ \ \ \ |-2y \\ 12=2y \ \ \ \ \ \ \ \ \ \ \ |\div 2 \\ y=6[/tex]
The answer is: 2 should be distributed as 2y + 12; y = 6.
Question 3:
[tex]3.3x-6.6=2.7x \ \ \ \ |-2.7x \\ 0.6x-6.6=0 \ \ \ \ \ \ \ \ |+6.6 \\ 0.6x=6.6[/tex]
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: [tex]\text{The solution is }0.6x=6.6[/tex]
Step-by-step explanation:
Part 1: Given the system of equations
[tex]n - 3m = 6[/tex] → (1)
[tex]n - 2m = 2[/tex] → (2)
Solving above two equations
Subtract 2 from 1, we get
[tex]n-3m-(n-2m)=6-2[/tex]
[tex]2m-3m=4[/tex]
[tex]m=-4[/tex]
(1) ⇒ [tex]n=3(-4)+6=-12+6=-6[/tex]
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
[tex]3.3x-2.7x=6.6[/tex]
[tex]0.6x=6.6[/tex]
Option 2 is correct.