Q. 44

# Solve for x and y:6(ax + by) = 3a + 2b,6(bx - ay) = 3b - 2a.

We have,

6(ax + by) = 3a + 2b

6ax + 6by = 3a + 2b …(i)

6(bx – ay) = 3b – 2a

6bx – 6ay = 3b – 2a …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply equation (i) by a and (ii) by b, so that variable y in both the equations have same coefficient.

Recalling equations 1 & 2,

6ax + 6by = 3a + 2b [×a]

6bx – 6ay = 3b – 2a [×b]

6a2x + 6b2x + 0 = 3a2 + 3b2

6(a2 + b2)x = 3(a2 + b2)

2x = 1

x = 1/2

Substitute x = 1/2 in equations (i)/(ii), as per convenience of solving.

Thus, substituting in equation (i), we get

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

3a + 6by = 3a + 2b

6by = 2b

y = 1/3

Hence, we have x = 1/2 and y = 1/3.

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