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.