Question 1 (vi)
Solve the following pairs of equations by reducing them to a pair of linear equations:
6x + 3y = 6xy
2x + 4y = 5xy
6x+3y=6xy
⇒6xxy+3yxy=6
⇒6y+3x=6...(i)
2x+4y=5xy
⇒2xxy+4yxy=5
⇒2y+4x=5...(ii)
Putting 1x=p and 1y=q in (i) and (ii) we get,
3p+ 6q - 6 = 0
4p +2q - 5 = 0
By cross multiplication method, we get
p−30−(−12)=q−24−(−15)=16−24
p−18=q−9=1−18
p−18=1−18 and q−9=1−18
p=1 and q=12
p=1x=1⇒x=1
q=1y=12⇒y=2
x=1, y=2
Hence, x=1 and y=2