Question

Whats the formula I use to solve questions like this?

4x + y = 13
x + 4y = -8

Answer 1

There's isn't a formula, per se. But there is a method that works every time. Do you want me to help you go through it?

Answer 2

definitely

Answer 3

@metalgearraiden Elimination?

Answer 4

Okay. So there are two different methods. One of them, as said above, is elimination, and the other is substitution. For this one, substitution is probably best, as we already have a variable that doesn't have a coefficient in front of it. Good so far?

Answer 5

i see, so i need to plug in the first part into the second?

Answer 6

Right. So we take the first and rewrite it as an equation of the form y=____________. Can you do that?

Answer 7

thats the part that im confused on, what to plug in. its going to be y = 4 - 13?

Answer 8

Not quite. To get the y alone, we're going to have to subtract 4x from both sides, right? So if we subtract 4x from both sides, what does it look like?

Answer 9

y = 4x(- 4) = -8 (-4)

Answer 10

?
oops 4y*

Answer 11

No, not quite. All I'm looking for is y=13-4x. See? We subtract 4x from both sides. Understand?

Answer 12

oh, so you just move the four over

Answer 13

with the x

Answer 14

Right. So now we plug that into the second equation and we get\[x + 4(13-4x) = -8\]You see where that came from?

Answer 15

y=13-4x
x4(13-4)=-8

just replace y. i see

Answer 16

Great. So now simplify. Simplify that equation down as much as you can. What do you get? You should get something like x = ________.

Answer 17

http://www.youtube.com/watch?v=KL5mZ1gArQE

Answer 18

@jdoe0001, people are on this forum for live help, not just the way to finish the problem.

Answer 19

x = 36 = -8. im a little stumped on the reduction part also.

Answer 20

Okay, I'll help you. Start by distributing the 4 to the terms in the parenthesis. Do you know what that means?

Answer 21

multiply 4 by both of them?

Answer 22

Right. So what does that give you?

Answer 23

52 and 16

Answer 24

Write out the expression with plus, minus, and variables.

Answer 25

x = 4 (13*4 - 4*4) = -8

Answer 26

I was thinking more like\[x + 52 - 16x = -8\]So\[-15x = -60\]So\[x=4\]See?

Answer 27

oh i took a step back. so after solving inside the parenthesis i can advance. how did you get the 15 out of that exactly?

Answer 28

It's \[x-16x = -15x\]Combining like terms. OK?

Answer 29

gotcha

Answer 30

is y=3 then?

Answer 31

Great. So from here on out it's easy - we have an x, so we plug it in somewhere to get a y.\[4(4) + y = 13\]So\[16 + y =13\]So \[y=-3\]So our solution is \[(4,-3)\]And we're done. Good?

Answer 32

i think i get it now

Answer 33

Great. Glad to help.

Answer 34

its appreciated

Answer 35

Since you asked for a formula, there is something called Cramer's rule in which you set up determinants and evaluate them. I think it is just as complex as the usual method. Still, do an iteret search for it.