Q23 of 186 Page 3

For what value of c, the following system of linear equations has infinite number of solutions:

cx + 3y – (c – 3) = 0, 12x + cy – c = 0

Given, pair of equations


cx + 3y – (c – 3) = 0


and 12x + cy – c = 0


On comparing the given equation with standard form i.e. a1 x + b1y + c1 = 0 and a2 x + b2y + c2 = 0, we get


a1 = c, b1 = 3 and c1 = – (c – 3)


and a2 = 12, b2 = c and c2 = – c


For infinitely many solutions,



Here,


∴ …(1)


On taking I and III terms, we get



⇒ c2 = 36


⇒ c = √36


⇒ c = ±6


But c = – 6 not satisfies the eqn (1)


Hence, the required value of c = 6.


More from this chapter

All 186 →
22

For what value of a, the following system of linear equations has no solutions:

3x + y = 1, (2a – 1) x + (a – 1) y = 2a + 1

 22

For what value of a, the following system of linear equations has no solutions:

(3a + 1) x + 3y – 2 = 0, (a2 + 1) x + (a – 2) y – 5 = 0

 23

For what value of c, the following system of linear equations has infinite number of solutions:

2x + 3y = 2, (c + 2) x + (2c + 1) y = 2 (c – 1)

 23

For what value of c, the following system of linear equations has infinite number of solutions:

x + (c + 1) y = 5, (c + 1) x + 9y = 8c – 1