Solve the pair of simultaneous equations
5x + 2y = 6
2x - 3y = 10
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Answer:
5x + 2y = 6 ------- (1)
2x - 3y = 10 -------(2)
We can solve by 2 methods.
Method 1: By elimination
(1) × 3: 15x + 6y = 18
(2) × 2: 4z - 6y = 20
(3) + (4): 19x = 38
Thus, x = 2
Substitute x = 2 into (1)
10 + 2y = 6
y = -2
Hence, the solution is x =2 , y = -2
Method 2: By substitution
From (1),
x = (6 - 2y) / 5 ------ (5)
Substitute (5) into (2)
2 × (6 - 2y) / 5 - 3y = 10
2 (6 - 2y) - 15y = 50
12 - 4y - 15y = 50
-19y = 50 - 12 = 38
y = -2
Substitute y = -2 into (5)
x = (6 - 2(-2)) / 5
x = 2
Hence, the solution is x =2 , y = -2
