Question

A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions. Is this statement true?
Always
Sometimes
Never

Answer 1

I'm not sure how to explain it to you but yes, it is always true.

Answer 2

the statement could never be true because As a linear Equation can cut Quadratic equation maximum at two points

hence maximum possible solutions are two

so its not possible to have infinite solution

Quadratic Equation :

f(x) = ax² + bx + c

Linear equation

f(x) = mx + d

Equating both

ax² + bx + c = mx + d

=> ax² + x(b-m) + c - d = 0

a form of Quadratic equation

hence maximum possible solutions are 2

Hence A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions is Never True