Question 1122737

please help with this problem  (500x+100y=325) (400x+150y=304)  
<pre>This is a perfect example of what NOT TO DO when solving a system with large numbers and possibly fractional solutions.
One of these 2 people is WRONG, as it's most likely attributable to the fact that both converted to decimals, which is TOTALLY UNNECESSARY, and as in most cases and this,
such "strategy," if you can call it that, can lead to possible confusion, and INCORRECT answers. This is the way it should be done:
500x + 100y = 325 ------ eq (i)
400x + 150y = 304 ------ eq (ii)
100x - 50y = 21 -------- Subtracting eq (ii) from eq (i) ------ eq (iii)
100x + 20y = 65 -------- Dividing eq (i) by 5 ------ eq (iv)
       70y = 44 -------- Subtracting eq (iii) from eq (iv)
{{{highlight_green(matrix(1,5, y, "=", 44/70, or, 22/35))}}}

Since it's too complex to substitute {{{matrix(1,3, 22/35, for, y)}}} (fraction that doesn't cancel nicely) into any of the 2 ORIGINAL equations - and could likely result in error(s) - we will ELIMINATE y as follows:
300x - 150y = 63 --- Multiplying eq (iii) by 3 ------- eq (v)
700x = 367 --------- Adding eqs (v) and (ii)
{{{highlight_green(matrix(1,3, x, "=", 367/700))}}}
You don't have to go further and convert the fractions to decimals. It's TOTALLY UNNECESSARY; plus, you were NOT asked to do so.