Given equations are
2x+my−4=0
3x−7y−10=10
Here a1=2,b1=m,c1=−4,a2=3,b2=−7,c2=−10
(i) When equations have a unique solution, then
a1a2≠b1b2
∴23≠m−7
⇒ m≠−143
(ii) When the equation have no solution, then
a1a2=b1b2≠c1c2
∴23=m−7≠−4−10
⇒ 23=m−7 (from first two terms)
⇒ m=−143