Q. 65.0( 1 Vote )

# For what value of k, the following pair of linear equations has infinitely many solutions?10x + 5y – (k – 5) = 020x + 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:

### Thevalue of k for which the system of equations has infinitely many solution is k = 10

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