3m-7n=-43
6m+5n=-10
Matrix is:
⌈3 -7 | -43 ⌉
⌊6 5 | -10 ⌋
To solve, find the determinant=3×5-(-7)×6=15+42=57.
Find the determinant for m:
⌈-43 -7 ⌉
⌊ -10 5 ⌋= -43×5-(-7)(-10)=-215-70=-285,
m=-285/57=-5.
Find the determinant for n:
⌈3 -43 ⌉
⌊6 -10 ⌋= 3(-10)-6(-43)=-30+258=228,
n=228/57=4.
CHECK
3m-7n=-15-28=-43,
6m+5n=-30+20=-10.
All OK.