Question

Solve the system of equations by substitution. What is the solution for x?
2x + y = 1

4x + 2y = -2


A.x=0
B.x=2
C.There is no x value as there is no solution.
D.x can be any value as there is an infinite number of solutions.

Answer 1

divide the second equation by 2

Answer 2

why would you divide

Answer 3

please do

Answer 4

So you divide every part by 2 or just a certain part

Answer 5

when you divide the second equation by 2, you divide every term in the equation by 2.

Answer 6

For example if I had
4x+6y=10
then I would get
2x+3y=5
after dividing by 2

Answer 7

2x+y=1

Answer 8

close,
(-2) divided by 2 = -1

Answer 9

So 2x+y=-1

Answer 10

So, when we divide
4x+2y=-2
by 2, we get
2x+y=-1

(yes, correct)

Answer 11

So, your new system is
2x+y=1 (your first equation)
2x+y=-1 (your second equation, after you divided it by 2)

Answer 12

So then we add the equation together

Answer 13

Now, tell me the following.

According to the first equation what is \(\normalsize\color{royalblue}{ \rm 2x+y }\) is equal to \(\normalsize\color{royalblue}{ \rm 1 }\).
According to the second equation what is \(\normalsize\color{royalblue}{ \rm 2x+y }\) equal to \(\normalsize\color{royalblue}{ \rm -1 }\).

Answer 14

Regardless of what number \(\normalsize\color{royalblue}{ \rm 2x+y }\) is, can it be equal to 1 and -1 at the same time ?

Answer 15

(if so, then 1=-1 )

Answer 16

So it would be C.There is no x value as there is no solution.

Answer 17

yes, there is no solution that satisfies the system
(i.e. these equations are parallel lines)

Answer 18

Thanks so much!!

Answer 19

anytime