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

Given :  A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions.

To find : Is given statement true? Always Sometimes Never

Solution:

A system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions.

This statement can never be true

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

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