2x + y = 5
3x +2y = 8
a1a2=23
b1b2=12
c1c2=−5−8=58
a1a2≠b1b2
Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations. By cross-multiplication method,
xb1c2−b2c1=yc1a2−c2a1=1a1b2−a2b1
x−8−(−10)=y−15+16=14−3
x2=1,y1=1
∴x=2,y=1