Solving equation values

Question

With the equations:

1. $7i_1 - 4i_2 = 50$
2. $12i_2 - 4i_1 = 20$

what is the method finding the values of $i_1$ and $i_2$? Both are integers. The answers are $i_1 = 10$ and $i_2 = 5$, how was it achieved.

Answer 1

Apply standard elementary algebra methods of elimination. You can divide the second equation by $4$ to get $$ i_1=3i_2-5. $$ Then insert into the first equation $$ 50=7(3i_2-5)-4i_2=17i_2-35. $$ By a lucky coincidence the solution of this is actually an integer.