If x = 2Y = 1 is the solution of the system of quadratic equations 32ax + by = 5AX − by = 2, find the value of a + 2B

Substituting x = 2Y = 1 into the equation system 32ax + by = 5AX − by = 2, 3A + B = 5, ① 2A − B = 2, ②, from ① - ②, a + 2B = 3, from ① + ②, 5A = 7, so a = 75, B = 45. So a + 2B = 3

When solving the equations {3a-2b = 6,5a + 3B = - 2 by the method of addition, subtraction and elimination, we can get ()

3a-2b=6… ①*3→9a-6b=185a+3b=-2… ② * 2 → 10A + 6B = - 4, the unknown B is eliminated, and 19A = 14, a = 14 / 19 is obtained

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