Question

How many solutions does the system of equation have? 3x=-12y+15 and x+4y=5

Answer 1

Ok so here are both of the equations graphed

Answer 2

That would make the answer 2?

Answer 3

(By the way, you can solve these by Substitution,Elimination, or Graphing, i'm solving by graph because it's the easiest right now)

Answer 4

It touches both y and x 1 time in the graph

Answer 5

The lines are on top of each other. You know that parallel lines have no solutions, how many do you think this has?

Answer 6

Ohhhhh so... the solution is how many times the 2 LINES touch each other; not the x or y axis?

Answer 7

When you do Substitution or Elimination, you're solving for the x and y variables. Those x and y variables are coordinates on where the 2 lines touch each other (x,y)

Answer 8

So it is infinitely because they are virtually the same line

Answer 9

Yes! =)

Answer 10

x-4y=12 and 5x-20y=60

Answer 11

Infinitely again

Answer 12

Yep.

Answer 13

You can tell it's infinite because if you do elimination, multiply the first equation by 5 and you see that they resemble each other and when subtracted will equal 0.

Answer 14

Ok I see that now. Thx!! y-6x=-3 and 4y-24x=-16 (last one)

Answer 15

would you multiply every digit by 24? How do you find the number of what to multiply the equations by?

Answer 16

No, you would just multiply the first equation by 4 so that the -6x turns into -24x, then subtract them to cancel out the x's and solve for y.

Answer 17

Oh! I see now!

Answer 18

the objective is to make the coefficient of one of the variable equal and opposite

Answer 19

what is the coefficient? What's the definition of that?

Answer 20

2x, the coefficient is 2 because it's infront of the x

Answer 21

and that rule applies ALWAYS?

Answer 22

And here is the graph to the last question you asked so you can check your ans

Answer 23

the 4 is the slope of the line? Correct?

Answer 24

Yes! I got it right! Thx!

Answer 25

Np, goodluck on any other =)

Answer 26

I understand that topic now

Answer 27

one of the 4 ways to solve simultaneous equations is the elimination/addition method. you eliminate one of the variable to get a linear equation. you have one unknown. solve for that variable then substitute the value in either of the original expressions for the other variable and get the other value.

Answer 28

Ok thnx!

Answer 29

I will be posting just a few more (different) questions

Answer 30

it is always a very good practice to check the solution because it is very very common to make mistakes (arithmetic error)