Question

Solve the following system of linear equations

using elimination method:

ax + by = 2a
^2
– 2b
^2

2x + y = 3a​

Answer 1

Answer:

6(ax + by) = 3a + 2b 

6ax + 6by = 3a + 2b  --------- (1)

6(bx - ay) = 3b - 2a

6bx - 6ay = 3b - 2a   ------------- (2)

On solving (1) * a & (2) * b, we get

6ax^2 + 6aby = 3a^2 + 2ab

6b^2x - 6aby = 3b^2 - 2ab

---------------------------------------

6ax^2 + 6b^2x = 3a^2 + 3b^2

6x(a^2 + b^2) = 3(a^2 + b^2)

x = 3/6

x = 1/2.

Substitute x = 1/2 in above equations, we get

6ax + 6by = 3a + 2b

6a(1/2) + 6by = 3a + 2b

3a + 6by = 3a + 2b

6by = 2b

y = 2b/6b

y = 1/3.