Question

Solve for x and y: px+qy=p-q qx-py=p+q

Answer 1

px+qy=p-q ---------(1)
qx-py=p+q ---------(2)
Multiplying (1) with p and (2) with q we get,
p²x+pqy=p²-pq -----------(3)
q²x-pqy=pq+q² -----------(4)
Adding (3) with (4) we get,
p²x+q²x=p²+q²
or, x(p²+q²)=p²+q²
or, x=1
Putting in (1) we get,
p.1+qy=p-q
or, qy=p-q-p
or, qy=-q
or, y=-1
∴, x=1 and y=-1

Answer 2

Answer:

Step-by-step explanation:

Given:

Px+Qy=P-Q......(1)

Qx-Py=P+Q......(2)

Now multiplying equation (1) with P and equation (2) with Q we get

Px+Qy=P-Q×P

Qx-Py=P+Q×Q

=P×Px+PQy=P×P-QP.....(3)

Q×Qx-PQy=P×Q+Q×Q....(4)

Now by adding equation (3) and (4) we get

(Psquare+Qsquare )x=Psquare+Qsquare

Implies x= Psquare+Qsquare /Psquar+Qsquare

Which implies x=1

Consider PX+Qy=P-Q

=P(1)+Q(y)=P-Q

=P+Qy=P-Q

=Qy=P-Q-P

=y=-Q/Q

=y=-1

Therefore the value of x=1 and y=-1