Question

Which values of P and Q result in an equation with no solutions? Px+40=Qx+20

Answer 1

The answer is 0, because if you made both P and Q zero, and then multiply them by x you’ll get zero. This will leave you with 40 = 20, which is not a solution.

Answer 2

When P and Q are equal there is no solution exist.

For example - (0,0) , (1,1)

Explanation:

Given : Equation
`Px+40=Qx+20`

To find : Which values of P and Q result in an equation with no solutions?

Solution :

In the given equation
`Px+40=Qx+20`

P, Q, x are variable.

We have to find the values at which the equation has no solutions.

`Px+40=Qx+20`

`Px+20=Qx`

`20=Qx-Px`

`20=x(Q-P)`

If Q=P then (Q-P)x = 0 for all x

Thus the original equation has no solutions.

For example,

Put x=1 and Q=1

`x+40=x+20`

`40\\eq 20`

There is no solution.