Question

for what values of p and q will the linear equation have infinitely many solutions 4x+5y=2, (2p+7q)x +(p+8q)y= 2q-p+1

Answer 1

here is your answer by Sujeet,
For infinitely number of solution,we must be have,a1/a2=b1=b2=c1/c2
a1/a2=b1/b2
4/2p+7q=5/p+8q
4p+32q=10p+35q
32q-35q=10p-4p
-3q=6p
q=6p/-3
q=-2p




then,
B1/b2=c1/c2
5/p+8q=2/2q-p+1
10q-5p+5=2p+16q
-5p-2p+10q-16q=-5
-7p-6q=-5
-7p-6(-2p)=-5
-7p+12p=-5
-7p+12p=-5
5p=-5
p=-5/5
p=-1



Now putting the value of q

q=-2p
q=-2*-1
q=2




value of p =-1
value of q=2



that's all....



that's all