Question

What is the solution of the system?
3x+3y=10
-9x-9y=-30

Answer 1

I multiplied the first eq. by 3 so I could eliminate a variable.
3(3x+3y=10)
9x+9y=30

A tried adding eq. 1 and 2 to eliminate a variable but then it would just be 30

Answer 2

u will get 18y = 60

Answer 3

how did you get that though?

Answer 4

9x+9y=30
-9x+9y=30
adding them
18y=60
-9xand 9x will get cancle
y=10/3

Answer 5

But the second equation is : -9x-9x=-30

Answer 6

you wrote it as: -9x+9y=30

Answer 7

And sorry, I meant -9x-9y=-30

Answer 8

ohh sorry i havent seen.....i only seen your multiplication

Answer 9

I don't know what I am doing wrong. b/c after looking at the equation again, all the numbers would cancel out

Answer 10

then there is no solution of these two lines because these are the eq of two parallel lines

Answer 11

I see, I don't like these problems haha they confuse me. I wish they all had an answer

Answer 12

Hmmm now look what happens if I just divide both sides of -9x-9y=-30 by -3

-3(3x + 3y) = -3(10)
3x + 3y = 10

Wow, I get the first equation. Must mean that both equations are the same. Thus infinite solutions.

Answer 13

ohh yup i m sorry these are coincident lines

Answer 14

@Hero can you help me understand what you did? and how you got that answer?

Answer 15

Before using substitution or elimination method, I always look to see if I can reduce the system first.

Answer 16

If one of your equations in a system look like

4x + 8y = 12

Clearly that can be reduced to

x + 2y = 3

Since each coefficient is divisible by 4

Answer 17

A better way to understand that is this

You have

4x + 8y = 12

4x + 8y factors to 4(x + 2y)

12 factors to 4*3

So 4x + 8y = 12 can be re-written as

4(x + 2y) = 4*3

Now you divide both sides by 4 to get
x + 2y = 3

Answer 18

You should be able to understand one of the two methods of reducing equations.

Answer 19

When they say "simplify first" before solving, that applies to systems of equations as well.

Answer 20

alright, they didn't say that in my lessons or in my tutor sessions. That is helpful.

Answer 21

There's all kinds of little tricks and methods you can use. To be honest, the Indians know all of the cyptic methods of approaching math that isn't taught here. If you want to really learn some solving methods get your hands on some of those Indian books like Quantitative Aptitude and learn the methods in it.

Answer 22

Of course, by "here" I assume you are American. I could be wrong though.

Answer 23

I am indeed an American haha thank you so much for helping. and thank you nirmalnema for helping also.

Answer 24

Simplifying first is sort of an unspoken rule of algebra. It is an implied step. Meaning, no one is going to explicitly tell you. It is just something you have to "see" for yourself during the solving process.

Answer 25

If you notice that something can be reduced on both sides of the equation or by cancelling factors of one, or by cancelling roots and exponents, then go ahead and do it. It will only make your life easier.

Answer 26

alright, thank you for telling me that haha it does make things much easier