Q. 7

# Solve for x and y: We have, …eq.1 …eq.2

Let us first simplify eq.1 & eq.2, by taking LCM of denominators,

Eq.1  9x – 2y = 108 …eq.3

Eq.2  3x + 7y = 105 …eq.4

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

Lets multiply eq.3 by 7 and eq.4 by 2, so that variable y in both the equations have same coefficient.

Recalling equations 3 & 4,

9x – 2y = 108 [×7

3x + 7y = 105 [×2

63x – 14y = 756

6x + 14y = 210

On adding the above the two equations we get,

69x + 0 = 966

69x = 966

x = 14

Substitute x = 14 in eq.3/eq.4, as per convenience of solving.

Thus, substituting in eq.4, we get

3(14) + 7y = 105

7y = 105 - 42

7y = 63

y = 9

Hence, we have x = 14 and y = 9.

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