Question

If am ≠ bl, then the system of equations
ax + by = c
lx + my = n
A. has a unique solution
B. has no solution
C. has infinitely many solutions
D. may or may not have a solution.

Answer 1

The system of equations is :

Given equation :

ax + by = c

lx + my = n

• Here, a1 = a, b1 = b, c1 = c and a2 = l, b2 = m, c2 = n

• Also given that, am ≠ bl

i.e a/l ≠ b/m

• a1/a2 ≠ b1/b2 is the condition for unique solution of system of linear equations.

• Hence equation is having unique solution

Answer 2

Answer:

ax+ by = c

lx + my = n

a1 = a. , a2= l

b1 = b. , b2= m

c1 = c. ,c2= n

it is given that,

am ≠ bl

therefore, a/l ≠ b/m

so, it has a unique solution

so, option a is a correct answer