(a) In the simultaneous equations : (px + qy = 5 ; qx + py = -10); p and q are constants. If x = 1 and y = -2 is a solution of the equations, find p and q.
(b) Solve : (frac{4r – 3}{6r + 1} = frac{2r – 1}{3r + 4}).
Explanation
(a) (px + qy = 5 )
When x = 1 and y = -2, we have
(p – 2q = 5 …. (1))
(qx + py = -10 )
When x = 1 and y = -2, we have
(q – 2p = -10 …. (2))
Multiplying (1) by -2, we have
(-2p + 4q = -10 … (1a))
(equiv 4q – 2p = -10)
(2) – (1a) : (q – 4q = -10 + 10)
(-3q = 0)
(q = 0)
Putting q = 0 in (1a), we have
(-2p = -10 implies p = 5)
Hence, p = 5 and q = 0.
(b) (frac{4r – 3}{6r + 1} = frac{2r – 1}{3r + 4})
((4r – 3)(3r + 4) = (2r – 1)(6r + 1))
(12r^{2} + 16r – 9r – 12 = 12r^{2} + 2r – 6r – 1)
(12r^{2} – 12r^{2} + 7r + 4r = – 1 + 12)
(11r = 11)
(r = 1).