Question

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

Answer 1

Let's solve for this algebraically, choose either the first or the second equation

Answer 2

1st

Answer 3

Wait not theres an easier way to do this lol

Answer 4

Which variable do you want to get rid of, x or y?

Answer 5

y

Answer 6

Right, so what are the common multiples for 2 and 3?

Answer 7

x and y?

Answer 8

Do you know what multiples are?

Answer 9

kinda sorta but not really

Answer 10

Numbers that can be divided by the number

So like 10 is a multiple of 2 because \(\frac {10}{5}\) is 2
Or any whole number multiplied by 2 ¯\_(ツ)_/¯

2,4,6,8,10,14 and so on

Answer 11

oh ok i get it

Answer 12

so 6 right?

Answer 13

I have you the ones for 2, can you give me for 3?

Answer 14

Yep

Answer 15

yay :)

Answer 16

Lets multiply the top equation by 3 and the bottom equation by -2 (To get them to cancel out)
\(~~~~3(3x + 2y = 8)=?\\
~\\
-2(2x + 3y = 2)=?\)

Can you solve both of these? (Distribute)

Answer 17

(9x + 6y = 8) = ?
(-4x + -6y = 2) = ?

Answer 18

Multiply the 3 and 8, the whole equation is being multiplied

Answer 19

oh ok yea

Answer 20

Same with the second equation

Answer 21

(9x + 6y = 24) = ?
(-4x + -6y = -4) = ?

Answer 22

right?

Answer 23

Right, now add both equations
\( ~~~~~~~~~~~~9x + 6y = 24 \\
~~+~-4x + -6y = -4 \\
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)

Answer 24

btw, i marked -2 before i asked the Q, meaning thats what i think it is. is that right?

Answer 25

Yeah its right

Answer 26

ok so all this wasnt even needed XD

Answer 27

ty anyway :)

Answer 28

Well this is the whole process if you want to know it ¯\_(ツ)_/¯

Answer 29

No problem

Answer 30

the next one is that last one and i didnt answer it meaning i really need help with this one..