In the simultaneous equation:px +qy=5,qx+py=-10;p and q are constant.If x=1 and y=-2 is a solution of the equa

Question

tion,find p and q.

Answer 1

put x=1 & y=-2 in both the equations
p-2q=5......(1)
q-2p=-10....(2)

Multiply (1) by 2
2p-4q=10...(3)

Add (2) & (3)
q-4q=-10+10
-3q=0
q=0

Put the value of q in (1)
p-0=5
p=5
Ans. p=5, q=0

Answer 2

Substitute x =1 and y=-2 into this pair of stimultaneous equations (px+qy=5 and qx+py=-10) respectively,
p*(1) + q*(-2) = 5
p- 2q = 5
p = 5+2q --- Equation1

q*(1) + p*(-2) = -10
q - 2p = -10 -- Equation 2

Substitute Equation1 into equation2,
we have
q - 2 (5+2q) = -10
q - 10 - 4q =-10
-3q = -10+10
- 3q = 0
q =0

Substitute q=0 into equation 1,
p = 5+ 2*(0)
p = 5

The solution to the above system is p=5 & q=0.

Answer 3

px +qy=5
qx+py=-10
if
x=1
y=-2
then

p1+q(-2)=5
q1+p(-2)=-10

or
p-2q=5
-2p+q=-10


multiply the first equation by 2
2p-4q=10
-2p+q=-10

-3q=0
q=0
p=5

5x=5
x=1

0x+5y=-10
5y=-10
y=-2

Answer 4

If x=1 and y=-2
px +qy=5,.............p -2q=5........... 2p -4q = 10
qx+py=-10...........q -2p = -10
by adding -3q = 0 .........q = 0 , so p = 5