Question

Write the number of solutions of the following pair of linear equations:

x + 2y – 8 = 0

2x + 4y = 16

Answer 1

The given equations are
x + 2y – 8 = 0                     ……(i)
2x + 4y – 16 = 0                   ……(ii)
Which is of the form `a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0`, where
`a_1 = 1, b_1 = 2, c_1 = -8, a_2 = 2, b_2 = 4 and c_2 = -18`

Now
`(a_1)/(a_2) = 1/2`
`(b_1)/(b_2) = 2/4 = 1/2`
`(c_1)/(c_2) = (−8)/(−16) = 1/2`
`⇒ (a_1)/(a_2) = (b_1)/(b_2) =(c_1)/(c_2 )= 1/2`
Thus, the pair of linear equations are coincident and therefore has infinitely many solutions.