Question

Solve for x and y:

i) 47x+31y=63; 31x+47y=15

ii) 99x+101y=499; 101x+99y=501

Answer 1

In these type of equations, where the coefficients of x and y are interchanged, rather than multiplying by the LCM , adding and subtracting them will give the correct answer without much calculation. For example in the first problem,
$47x + 31y = 63 \\ 31x + 47y = 15 \\ 78x + 78y = 78 \\ x + y = 1$
and
$47x + 31y = 63 \\ 31x + 47y = 15 \\ 16x - 16y = 48 \\ x - y = 4$

Now you have two simple equations, which can be easily solved.
$x + y = 1 \\ x - y = 4 \\ 2x = 5 \\ x = \frac{5}{2} \\ y = \frac{ - 3}{2}$
The second problem has the same solution and is left to you for practice!!

Hope this helps and if it does please mark it as the brainliest answer, I would really appreciate it!!!!!