Question

Find an ordered pair that is a solution of the system
4 2 1
3 2 3
x y
x y
+ = -


 - =

Answer 1

What the..? Wait.

Answer 2

4x+2y=-1
3x-2y=3

Answer 3

Add the equations together and what do you get?

Answer 4

Hmm

Answer 5

How do I add them?

Answer 6

Combine all of the like terms. Since you know that 4x+2y=-1 and 3x-2y=3, you also know that 4x+2y + 3x -2y = -1 + 3

Answer 7

so, x=2/7 ?

Answer 8

good work =)

Answer 9

now how do you get y when x=2/7?

Answer 10

umm, i think you just substitute right? O.o

Answer 11

yep =) [just plug x=2/7 back into either equation]

Answer 12

Yay! This is easy =D Thank youu.

Answer 13

No problem. Now the general way to solve these types of problems (systems of equations), is to solve for one variable first, and then substitute back into the other equation. To do this, you mus have a separate equation for each unknown variable - for example in this problem there are two equations and two unknowns.

Answer 14

Yes I get it! But for example you have like:

4x+4y=-1
3x-2y=3

What do you do here? you can't cancel the 'y' or 'x' out

Answer 15

well, you actually can if you know a small trick.

Answer 16

if you know that 3x - 2y = 3, you can multiply both sides by the same number and the equation will still be true (equivalent)

Answer 17

in this case, I can multiply both sides by 2

Answer 18

so 2(3x -2y) = 2*3

Answer 19

6x - 4y = 6

Answer 20

Now you can cancel out all of the y's by adding the two equations

Answer 21

4x + 4y = 4
6x - 4y = 6

Answer 22

Aooh! *smart* :P :D

Answer 23

I like it! Thanks a lot for the help.

Answer 24

No problem. There are other ways to solve these types of problems, but just ask here when you find a case where it's hard to find a way to cancel out =). good luck!

Answer 25

btw, the ordered pairs are :

(0,-5/14) and (2/7,0) ?