Question

for which value of A do the pair of linear equation Ax +y =A*A and x + A y =A*A (A) no solution (b) infinite many solutions (c) unique solution

Answer 1

a) for no solution,condition of coefficient of equation
a1/a2=b1/b2=/c1/c2
A/1=1/A=/1/1
on Cross Multiplication
A^{2}=1
A=+-1
b) for infinite many solution
a1/a2=b1/b2=c1/c2
A/1=1/A=1/1
on Cross Multiplication
A^{2}=1
A=+-1
A/1=1
A=1
so for infinitely many solution A=1
c) for unique solution
a1/a2=/ b1/b2
A/1 =/1/A
A^{2}=/1
A=/ +-1
symbol =/ is used for not equal