C=3d-27 and 4d + 10c=120?

whats d and c i cant figure it out and both equations must have the same number


so


3 x d - 27 = c


4 x d + 10= c


what does c and d equal?

C=3d-27 and 4d + 10c=120?
4d + 10c=120


4d + 10(3d-27)=120


4d + 30d - 270=120


4d + 30d = 390


34d = 390


d = 390/34





c=3d-27


c=3(390/34)-27


c=126/17
Reply:The easiest way I know to solve these is to look at the two equations you were given. You were told what c equals. Substitute that everywhere you have c, like this:





4d + 10c =120 becomes


4d +10(3d-27) = 120


then just do the math and solve for d. After you get d, solve the first equation for c. And you've got both answers.
Reply:Well, there are a few ways to do systems of equations. The first 2 answers showed it doing substitution, I've always preferred linear combination, so I'll show the work that way.





First i put both equations in general form, so you have





4d + 10c = 120


-3d + c = - 27





Well, by looking at those, there are a few ways to do it, but I would multiply the bottom equation by 10, so you have both equations with 10c, then subtract..... as follows





4d + 10c = 120


-30d + 10c = -270


________________


34 d = 390





d = 195/17





sub back in to either one... for simplicity use...


c = 3d - 27


c = 3(195/17) - 27


c = (585/17) - 27


c = (585/17) - (459/17)


c = 126/17





Granted, the way the first answer was done was probably the easiest way, since one of the problems is set up as c = which makes it ideal for substitution, though I prefer linear combination just because it ends up being easier in most situations, so its just the way I like to do it.

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