Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The value(s) of m does the system of equations 3x + my = m and 2x – 5y = 20 has a solution satisfying the conditions x > 0, y > 0
A
M ∈ (0, ∞ )
B
M ∈ 
∪ (30, ∞ )
∪ (30, ∞ )
C
M ∈ 
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
By using Cramer’s rule, the solution of the system is
x = 
, y = 
, where Δ = 
= –(15 + 2m)
Δ x = 
= –25m, Δ y = 
= 60 – 2m
⇒ x = 
= 
> 0,
for m > 0, or m < 
.
Also y = 
= 
>0
for m > 30, or m < 
.
⇒ x > 0, y > 0 for m > 30 or m < 
For m = 
, the system has no solution.
Hence is correct answer.
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