Question

x + ay = 1 and ax + y = 2

Answer 1

Answer:concepts : if and are two linear equations.

equations have no solution when

equations have infinitely many solutions when

equations have an unique solution when

here equations are ; ax + y - a² = 0 and x + ay -1 = 0

for no solution

a/1 = 1/a ≠ -a²/-1

or, if a = -1 then, -1/1 = 1/-1 ≠ -(-1)²/-1

hence, a = -1

for infinitely solutions

a/1 = 1/a = -a²/-1

or, a/1 = 1/a = a²/1

a/1 = a²/1 => a(a - 1) = 0, a = 0, 1

1/a = a²/1 => a³ -1 = 0, a = 1

common value of a is 1

so, value of a will be 1

for an unique solution

a/1 ≠ 1/a

or, a² ≠ 1

or, (a² - 1) ≠ 0

or, a ≠ -1 and 1

hence, a belongs to all real numbers except 1 and -1

we can write it ,

Step-by-step explanation: