Question

Solve using the substitution method-3x + y = 4

x + 3y = 22 any help would be greatly appriciated i am having such a hard time with this. I just can not grasp the concept

Answer 1

Which variable do you want to substitute for, the x or the y?

Answer 2

It is your choice, either one is OK.

Answer 3

the x

Answer 4

Good choice. Looking at the two equations, I would use the second one as x appears by itself. x + 3y =22. First subtract 3y from both sides getting x=22-3y Are you with me so far?

Answer 5

yes

Answer 6

O.K. this next step is tricky. We are going to substitute for x in the first equation. x is 22-3y as calculated above. Careful with the negative sign before the x in that first equation. Here is what it is going to look like:
-(22-3y) +y =4
-22 +3y +y = 4 Did you follow that, note how the minus sign worked.

Answer 7

yes

Answer 8

Now we simplify by combining similar terms getting -22 + 4y =4
Now we add 22 to both sides getting 4y=26
to solve for y, we divide both sides by 4 getting y=26/4 or 13/2

Answer 9

Now that we have the value for y we can plug that value in the second equation and figure out what x is.
x + 3y=22 (2nd equation)
x +3(13/2)=22
x +39/2 =22 now subtract 39/2 from both sides getting
x=22 - 29/2
x=44/2 - 29/2 =15/2 or 7 1/2

Answer 10

To check for mistakes substitute both values in 2nd equation
x+3y =22
7/12 +3(13/2)=22
7/12 +39/2 =22
7/12 + 234/12 =241/12= OOOOPS there is a mistake and it is in the post above I will redo it.

Answer 11

Now that we have the value for y we can plug that value in the second equation and figure out what x is.
x + 3y=22 (2nd equation)
x +3(13/2)=22
x +39/2 =22 now subtract 39/2 from both sides getting
x=22 - 39/2
x=44/2 - 39/2 =5/2 or 2 1/2

Answer 12

Back to the check: x + 3y = 22
5/2 + 3(13/2) =22
5/2 +39/2 =22
44/2=22
22=22 There that is better.

Answer 13

The mistake was I changed 39 to 29 for no good reason. Good luck with these.