Question

Show that the system equations
2x - 3y = 5,
6x - 9y = 15

has an infinite number of solutions

Answer 1

The given system of equations:
2x - 3y = 5
⇒ 2x - 3y – 5 = 0            ….(i)
6x - 9y = 15
⇒6x - 9y - 15 = 0              …(ii)
These equations are of the following forms:
`a_1x+b_1y+c_1 = 0, a_2x+b_2y+c_2 = 0`
Here, `a_1 = 2, b_1= -3, c_1= -5 and a_2 = 6, b_2= -9, c_2= -15`
`∴ (a_1)/(a_2) = 2/6 = 1/3 ,(b_1)/(b_2) = (−3)/(−9) = 1/3 and (c_1)/(c_2 )= (−5)/(−15) = 1/3`
Thus, `(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`
Hence, the given system of equations has an infinite number of solutions.