Question

What is the value of the x variable in the solution to the following system of equations?
2x + 2y = 6
x + 3y = −1

a. −2
b. 2
c. 5
d. −5

Answer 1

Can someone please walk me through how to do this

Answer 2

first equation times 3 and second equation times -2

(2x + 2y = 6) × 3
(x + 3y = −1) × (-2)

this will get you a new (but equivalent to the previous) system of equations.

6x + 6y = 18
-2x - 6y = 2

now add the equations and solve for x

Answer 3

So you just take one of the equations and multiply it to the other equation?

Answer 4

first equation divide each term by 2

Answer 5

Would it be x+y=6 then?

Answer 6

I didnàt multiply equation times equation, all I did is that I multiplied each term in the equation times some number.... i did this for both of the equations, and choose the numbers by which to multiply in a way that would eliminate the y (since the variable you need is x).

Answer 7

So you would come up with 6x+6y= 18? for the first equation and

-2x+-6=2?

Answer 8

-2x - 6y = 2
for the second equation, you meant (right ?)

Answer 9

Sorry yes thats what I meant

Answer 10

yes, that is what you inded come up with.

Answer 11

itàs ok...)

Answer 12

Now, add the equations

Answer 13

6x + 6y = 18
-2x - 6y = 2

Answer 14

Okay so it would be 4x + 18y = 20?

Answer 15

Oh wait 12y*

Answer 16

18y?

Answer 17

no, not 12.

when you add 6 and -6 you get
6+(-6)=6-6=0

and so when you add 6y and -6y
you get (6y)+(-6y)=??

Answer 18

Oh so it would be 4x = 20?

Answer 19

so x is?

Answer 20

5?

Answer 21

yes, that is correct!

Answer 22

Thank you so much! That makes a lot more sense now!

Answer 23

very nice to hear that... you are welcome!