how to solve this??? Find the solutions for the two equations 5x + 6y = 54 15x + 18y = 162 can this even be solved?
Um... I don't think it can be solved... 5x + 6y = 54 is just 15x + 18y = 162 simplified. They're the same equation... so if you tried to use one to solve for the other, you'd just get 0 = 0. But I haven't had algebra in like 3 years, so I could be wrong.
An easier way to solve simultaneous equations, is to convert them into matrix form. That is, x y 5 6 I 54 15 18 I 162 You then can alter each row by either adding, subtracting, multiplying or dividing. The end result that you would want is something along the lines of x y 1 0 I 203 (random number) 0 1 I 234 (random number) The I is just a divider, an easier from of =. So x will = 203 and y will = 234. That technique is really useful if you have many simultaneous equations. I've had to solve 10 simultaneous equations at one time! With the matrix form, it's not so bad. But yeah, in this case, if you multiply row 1 by 3, and subtract it from row 2, you will just end up with x y 15 18 I 162 0 0 I 0 So when answering that simultaneous equation, you would say that it has infinite solutions.