Question

solve simultaneous equation by substitution method 3x+2y=12, 4x-3y=1

Answer 1

substitution is not the ideal way for this example, but anyway.....

from 3x+2y = 12 ---> y = (12-3x)/2
sub into the 2nd:
4x - 3(12-3x)/2 = 1
multiply by 2
8x - 3(12-3x) = 2
8x - 36 + 9x = 2
17x = 38
x = 38/17
then y = (12 - 3(38/17))/2
= (12 - 114/17)/2
= 6 - 57/17 = 45/17

I would have done the following using elimination:

1st times 3 ----> 9x + 6y = 36
2nd times 2 ----> 8x - 6y = 2

add them: 17x = 38
x = 38/17

sub into 1st:
3(38/17) + 2y = 12
2y = 12 - 114/17 = 90/17
y = 45/17

The final fractional answers of course could not be avoided, but
getting there involved less fractional work.

Answer 2

20 x, 50=y