For what value of k, the following pair of linear equations has infinitely many solutions?
10x + 5y – (k – 5) = 0
20x + 10y – k = 0
Given:
Equation 1: 10x + 5y = (k – 5) Equation 2: 20x + 10y = k
Both the equations are in the form of :
a1x + b1y = c1 & a2x + b2y = c2 where
a1 & a2 are the coefficients of x
b1 & b2 are the coefficients of y
c1 & c2 are the constants
For the system of linear equations to have infinitely many solutions we must have
………(i)
According to the problem:
a1 = 10
a2 = 20
b1 = 5
b2 = 10
c1 = k – 5
c2 = k
Putting the above values in equation (i) we get: