Question

If (–5, –5) is the solution of the system of equations
3x + 4y + 2p – q = 0 and 4x + 3y + q – 3r = 0,
then r is always equal to

Answer 1

(-5,-5)  is the solution of the system of equations 3x+4y+2p-q=0 and 4x+3y+q-3r=0
Then,
3(-5)+4(-5)+2p-q=0
or, -15-20+2p-q=0
or, 2p-q=35 -------------(1) and
4(-5)+3(-5)+q-3r=0
or, -20-15+q-3r=0
or, q-3r=35 --------------(2)
Subtracting (2) from (1) we get,
2p-2q+3r=0
or, 3r=2q-2p
or, r=2(q-p)/3