i The given simultaneous equations are
6x – 4y = -12
∴ 3x – 2y = -6 …(i) [Dividing both sides by 2]
8x – 3y = -2 …(ii)
Equations (i) and (ii) are in ax + by = c form. Comparing the given equations with
a1x + b1y = c1 and a2x + b2y = c2 , we get
a1 = 3, b1 = -2, c1 = -6 and
a2 = 8, b2 = -3, c2 = -2
∴ (x, y) = (2, 6) is the solution of the given simultaneous equations.
ii. The given simultaneous equations are
4m + 6n = 54
2m + 3n = 27 …(i) [Dividing both sides by 2]
3m + 2n = 28 …(ii)
Equations (i) and (ii) are in am + bn = c form. Comparing the given equations with
a1m + b1n = c and a2 m + b2 n = c2 , we get
a1 = 2, b1 = 3, c1 = 27 and
a2 = 3, b2 = 2, c2 = 28
∴ (m, n) = (6, 5) is the solution of the given simultaneous equations.
iii. The given simultaneous equations are
2x + 3y = 2 …(i)
x =\(\frac{y}{2}\) =\(\frac{1}{2}\)
∴ 2x – y = 1 …(ii) [Multiplying both sides by 2]
Equations (i) and (ii) are in ax + by = c form. Comparing the given equations with
a1x + b1y = c1 and a2x + b2y = c2 , we get
a1 = 2, b1 = 3, c1 = 2 and
a2 = 2, b2 = -1, c2 = 1