Page 9 - LN

Example 2: Solve the following system of equation by cross multiplication method:
ax + by = a - b
bx - ay = a + b

Solution: The given equations can be written as
ax + by - (a - b) = 0
bx - ay - (a + b) = 0

a 1 = a, b 1 = b, c 1 = -(a - b)
a 2 = b, b 2 = -a, c 1 = -(a + b)

By cross multiplication, we get,

or

x =

y =
Hence, the solution is x = 1, y = -1

Example 3: Find the value of k for which the following system of linear equations will
have no solution
3x + y = 1
(2k - 1)x + (k - 1)y = 2k + 1

Solution: The given system of equations is 3x + y = 1
(2k - 1)x + (k - 1)y = 2k + 1
Here,
a 1 = 3, b 1 = 1, c 1 = -1,
a 2 = 2k - 1, b 2 = k - 1, c 2 = -(2k + 1 )

For the system to have no solution, we must have,

9