If y ≠ 1, is x = 1 ?
x² + y² = 1, y = 1 - x

Solution :

Given: Linear equations in two variables are x² + y² = 1 --- (a)

y = 1 - x --- (b)

Using the substitution method we put eq(b) in eq(a), we get

x² + (1 - x)² = 1

x² + 1 - 2x + x² = 1

2x² - 2x = 0

2x(x - 1) = 0

x = 0 and x = 1

Hence, x = 1

If y ≠ 1, is x = 1 ?
x² + y² = 1, y = 1 - x

Summary :

If y ≠ 1, x² + y² = 1 and y = 1 - x then x = 1.