Question

What is the value of the y variable in the solution to the following system of equations?

3x + y = 11
-3x + 2y = 1

2
4
y can be any number as there are infinitely many solutions to the system.
There is no y value as there is no solution to the system.

Answer 1

Well the easiest way to solve this would be to solve the first equation for x where y is the variable and plug that into the second equations so you will instantly solve for y.

Answer 2

Can you walk me through it

Answer 3

@lasttccasey

Answer 4

Sure, first take the first equation, 3x + y = 11, and solve it for x. So make this equation in the form x = ...

Answer 5

3x=11-y
3x/3=11/3-y ? @lasttccasey

Answer 6

x=11/3-y ?

Answer 7

Almost. Don't forget the y is also divided by 3. So x = 11/3 - y/3

Answer 8

Next you will just plug this into equation two for the x variable, there by getting rid of all x's.

Answer 9

-3(11/3-y/3) + 2y = 1 @lasttccasey

Answer 10

Yes now multiply the -3 through the parenthesis, combine like terms, and solve for y. Then you're done!

Answer 11

(-33/3+3/3) +2y=1
-11+2y=1
2y=1+11
2y=12
2y/2=12/2
y=6

Answer 12

@lasttccasey

Answer 13

But thats no answer

Answer 14

Be careful with your math.
-3(11/3-y/3) + 2y = 1
Will become:
-11+ y + 2y = 1

Answer 15

(-33/3+3/3) +2y=1
-11+y+2y=1
3y=12
y=4

Answer 16

Thanks @lasttccasey !

Answer 17

You're welcome! @HishamNafiseh