Q25 of 186 Page 3

Find the value of a for which the following system of equations has unique solution:
ax + 2y = 5, 3x + y = 1

Given, pair of equations

ax + 2y = 5

and 3x + y = 1

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

a₁ = a, b₁ = 2 and c₁ = – 5

and a_{2 =} 3, b₂ = 1 and c₂ = – 1

For unique solutions,

Here,

I II

On taking I and II terms, we get

⇒ a≠6

Thus, given lines have a unique solution for all real values of a, except 6.

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

(c – 1) x – y = 5, (c + 1) x + (1 – c) y = 3c + 1

Solve the following system of equations graphically. Also determine the vertices of the triangle formed by the lines and y – axis.

4x – 5y – 20 = 0, 3x + 5y – 15 = 0

Find the value of a for which the following system of equations has unique solution:

9x + py – 1 = 0, 3x + 4y – 2 = 0

Find the value of a for which the following system of equations has unique solution:

3x + 2y = 4, ax – y = 3

Find the value of a for which the following system of equations has unique solution:ax + 2y = 5, 3x + y = 1