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Q12 of 244 Page 124

For what value of k does the system of equations
kx + 2y = 5, 3x – 4y = 10

have (i) a unique solution, (ii) no solution?

(i) Given: kx + 2y = 5 – eq 1

3x – 4y = 10 – eq 2

Here,

a₁ = k, b₁ = 2, c₁ = 5

a₂ = 3, b₂ = - 4, c₂ = 10

Given systems of equations has a unique solution

∴ ≠

≠

- 4k 6

k ≠

∴ k ≠

(ii) Given: kx + 2y = 5 – eq 1

3x – 4y = 10 – eq 2

Here,

a₁ = k, b₁ = 2, c₁ = 5

a₂ = 3, b₂ = - 4, c₂ = 10

Given that systems of equations has no solution

∴ =

Here,

=

Here,

- 4k = 6

∴

More from this chapter

10

Show that the system of equations

2x – 3y = 5, 6x – 9y = 15

11

Show that the system of equations

6x + 5y = 11, 9x + y = 21

13

For what value of k does the system of equations

x + 2y = 5, 3x + ky + 15 = 0

have (i) a unique solution, (ii) no solution?

14

For what value of k does the system of equations

x + 2y = 3, 5x + ky + 7 = 0

have (i) a unique solution, (ii) no solution?

Also, show that there is no value of k for which the given system of equations has infinitely many solutions.