Question

Answer 12th question plz

Answer 1

Answer:

p=6

Step-by-step explanation:

The equations have infinitely many solutions only if they represent the same line.

The line represented by px + py = 12 has gradient -p/p = -1.

We need the gradient of the second line to be -1, too.  So

-( p - 3 ) / 3 = -1  =>  p - 3 = 3  =>  p = 6

So we need p = 6 for the lines to be parallel.

So far, we know that if the problem has an answer at all, it must be p = 6.  But it's possible that the question has a mistake (or a trap) and there is NO p that works.  This is because parallel is not enough to be sure that they're the same line.  We need to check...

Putting p = 6 into the equations, they become:

3x + 3y = 6  <=>  x + y = 2

and

6x + 6y = 12  <=>  x + y = 2

Good... they are the same line, so there are infinitely many solutions.