Question

1. When solving a system of equations how do you know which method to use? 2. Solve the system of equations below and explain the method you used and show the steps you used.
–y + 3x = 6
y = –6x + 12
Please explain it because I'm really confused on this.

Answer 1

the method you use is the one that you are most comfortable with .... method is only for user functionality

Answer 2

spose we use elimination

–y + 3x = 6
y = 12 - 6x
-----------------
3x = 18 - 6x ; solve for x, to determine y

if we use substitution

–y + 3x = 6
y = 12 - 6x <-- it is already known that y = some function of x
so sub it into the other one


–(12-6x) + 3x = 6 ; and soplve for x to determine the value of y

Answer 3

I don't really understand it still. can you try and explain how to do solve the equation better?

Answer 4

R1: 3x-y=6
R2: 6x+y=12
solve this by using elimination method
R2+R1 => 9x = 18 => x=2
and then replace x=2 into R1 or R2 and solve for y

Answer 5

Oh my gosh guys I'm so confused! I'm having a lot of trouble in math right now. Can you like label each step and expalin it? Please. I know I probably sound stupid since i cant fiqure this out when you gave me the answer.

Answer 6

are you comfortable with being able to solve for a single variable?

Answer 7

Yeah liek yo mean in a normal equation?

Answer 8

yep

Answer 9

the idea is to reduce this setup to a single variable that can be solved; and once you know the value of one of the variables, that can be used to determine the value of the other one

Answer 10

the method of substitution is simply defining one variable in terms of the other;

notice that one equation they give you already defines y in terms of x

y = –6x + 12 ; so no matter what y equals at the moment, it is completely dependant on the value of x; whereever we see a y, we can replace it by the equation that defines it; does that make sense?

Answer 11

Yeah

Answer 12

so lets take a look at the other equation they provide; and see if there is a y variable in it that we can redefine by its equation in x

–y + 3x = 6
^
theres a y, lets replace it

–(-6x+12) + 3x = 6 ; now we have a setup that we can solve for a single variable right?

Answer 13

Yeah it makes a lot more sense now.

Answer 14

once we have a solid value for x; we can use it to define y :) since:

y = -6x+12 right?

Answer 15

Yeah so you just solve the one equation to find x then you solve y=-6+13 to find y and then you right the answer like (x,y) right?

Answer 16

exactly ;)

Answer 17

Okay thanks. I get it now.

Answer 18

youre welcome, and good luck ;)