Q1) Find the values of p and q for which the system of equations have infinite number of solutions.
2x+3y=7, (p+q+1)x+(p+2q+2)y=4(p+q)+1.
Q2) Solve the following pair of equations by cross-multiplication method
a²x+b²y=c² and b²x+a²y=d²
Q3) 8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken to finish the work by one man alone.

Asked by mkmishra101 | 18th Jun, 2016, 05:26: PM

Expert Answer:

begin mathsize 12px style Kindly space ask space one space question space at space straight a space time.
2 straight x plus 3 straight y equals 7 space and space left parenthesis straight p plus straight q plus 1 right parenthesis straight x plus left parenthesis straight p plus 2 straight q plus 2 right parenthesis straight y equals 4 left parenthesis straight p plus straight q right parenthesis plus 1
Since space the space system space of space equations space has space infinite space number space of space solutions comma
fraction numerator 2 over denominator straight p plus straight q plus 1 end fraction equals fraction numerator 3 over denominator straight p plus 2 straight q plus 2 end fraction equals fraction numerator 7 over denominator 4 left parenthesis straight p plus straight q right parenthesis plus 1 end fraction
So comma space fraction numerator 2 over denominator straight p plus straight q plus 1 end fraction equals fraction numerator 3 over denominator straight p plus 2 straight q plus 2 end fraction space and space fraction numerator 3 over denominator straight p plus 2 straight q plus 2 end fraction equals fraction numerator 7 over denominator 4 left parenthesis straight p plus straight q right parenthesis plus 1 end fraction
rightwards double arrow 2 straight p plus 4 straight q plus 4 equals 3 straight p plus 3 straight q plus 3 rightwards double arrow straight p minus straight q equals 1 space and space
12 straight p plus 12 straight q plus 3 equals 7 straight p plus 14 straight q plus 14 rightwards double arrow 5 straight p minus 2 straight q equals 11
straight p minus straight q equals 1 rightwards double arrow straight p equals 1 plus straight q
Substitute space straight p space equals space 1 space plus space straight q space in space 5 straight p minus 2 straight q equals 11 comma space we space get
5 left parenthesis 1 plus straight q right parenthesis minus 2 straight q equals 11 rightwards double arrow 5 plus 5 straight q minus 2 straight q equals 11 rightwards double arrow 3 straight q equals 6 rightwards double arrow straight q equals 2
Thus comma space the space value space of space straight p space equals space 1 space plus space straight q space equals space 1 space plus thin space 2 space equals space 3
Hence space straight p space equals space 3 space and space straight q space equals space 2. end style

Answered by Rebecca Fernandes | 18th Jun, 2016, 07:29: PM