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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?
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?
i see, so i need to plug in the first part into the second?
Right. So we take the first and rewrite it as an equation of the form y=____________. Can you do that?
thats the part that im confused on, what to plug in. its going to be y = 4 - 13?
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?
y = 4x(- 4) = -8 (-4)
? oops 4y*
No, not quite. All I'm looking for is y=13-4x. See? We subtract 4x from both sides. Understand?
oh, so you just move the four over
with the x
Right. So now we plug that into the second equation and we get\[x + 4(13-4x) = -8\]You see where that came from?
y=13-4x x4(13-4)=-8 just replace y. i see
Great. So now simplify. Simplify that equation down as much as you can. What do you get? You should get something like x = ________.
@jdoe0001, people are on this forum for live help, not just the way to finish the problem.
x = 36 = -8. im a little stumped on the reduction part also.
Okay, I'll help you. Start by distributing the 4 to the terms in the parenthesis. Do you know what that means?
multiply 4 by both of them?
Right. So what does that give you?
52 and 16
Write out the expression with plus, minus, and variables.
x = 4 (13*4 - 4*4) = -8
I was thinking more like\[x + 52 - 16x = -8\]So\[-15x = -60\]So\[x=4\]See?
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?
It's \[x-16x = -15x\]Combining like terms. OK?
is y=3 then?
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?
i think i get it now
Great. Glad to help.
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.