Solve for x and y:
Since, if a = b = c ⇒ a = b & b = c
Thus, we have
and
Lets simplify these equations. We can rewrite them,
⇒ 3(x + y – 8) = 2(x + 2y – 14)
⇒ 3x + 3y – 24 = 2x + 4y – 28
⇒ 3x – 2x + 3y – 4y = - 28 + 24
⇒ x – y = - 4 …(i)
⇒ 3(3x + y – 12) = 11(x + 2y – 14)
⇒ 9x + 3y – 36 = 11x + 22y – 154
⇒ 11x – 9x + 22y – 3y = 154 – 36
⇒ 2x + 19y = 118 …(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply eq.(i) by 19, so that variable y in both the equations have same coefficient.
Recalling equations (i) & (ii),
x – y = - 4 [×19
2x + 19y = 118
⇒ 21x = 42
⇒ x = 2
Substitute x = 2 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(i), we get
2 – y = - 4
⇒ y = 2 + 4
⇒ y = 6
Hence, we have x = 2 and y = 6