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What is the value of the x variable in the solution to the following system of equations? 3x + 2y = 8 2x + 3y = 2 4 –2 x can be any number as there are infinitely many solutions to this system. There is no x value as there is no solution to this system.

2. Callisto

Multiply the first equation by 3, what do you get?

6?

4. Callisto

No? Multiply both sides of the first equation by 3: 3 (3x + 2y) = 3 (8) ^Simplify this

ohhh right

hmmm....4?

7. Callisto

How do you get 4 from doing the multiplication?

i was guessing the answer

9. Callisto

Perhaps we can solve it together, rather than just guessing it?

okay we can try but i dont get this at all

11. Callisto

Let see how it goes :) First, multiply both sides of the first equation by 3, we get 3 (3x + 2y) = 3 (8) 9x + 6y = 24 Do you get this part so far?

yes

13. Callisto

Just call that equation (9x + 6y = 24) as (a) Now, we multiply the second equation 2x + 3y = 2 by 2, what do you get?

wait what's y?

15. Callisto

We will calculate it if you want. But in this case, we are going to solve the system of equations by elimination. And the variable we are going to eliminate is y.

i think i need a bit more of a push

17. Callisto

Hmm.. What do you mean?

towards getting the answer, i dont quite understand as well as i would like to

19. Callisto

Actually, we'll get the answer quite soon... A few more steps to go :| What do you get when you multiply the second equation 2x + 3y = 2 by 2?

10? :/

21. Callisto

Still guessing the answer?

no im just not sure

23. Callisto

10 for the answer or is that what you get when you do the multiplication?