Question

Which values of P and Q result in an equation with exactly one solution? Qx-6=Px-103

Answer 1

For any value of P & Q except when both are equal , we get One solution of equation.

Explanation:

Given: Linear Equation, Qx - 6 = Px - 103

This equation has exactly 1 solution.

To find: Value of P and Q

First we solve the linear equation for value of x,

Qx - 6 = Px - 103

Transpose Px to LHS ( Left hand side ) we get,

Qx - Px - 6 = -103

Transpose 6 to RHS ( Right hand side ) we get,

Qx - Px = -103 + 6

Qx - Px = -97

taking x common in LHS, we get

( Q - P ) x = -97

Traspose ( Q - P ) to RHS, we get

`x=(-97)/(Q-P)`

`x=(-97)/(-(P-Q))`

`x=(97)/(P-Q)`

Thus, we are get only 1 value of x but it exist if P ≠ Q

otherwise no solution exist for the given linear Equation.

Therefore, For any value of P & Q except when both are equal , we get One solution of equation.

Answer 2

Any values such that P ≠ Q will give an equation with exactly one solution.