If x = 1, y = - 1 and x = 3Y = - 5 are solutions of the equation AX + by + 2 = 0 about X and y, try to judge whether x = - 4 and y = 9 are solutions of the equation AX + by + 2 = 0? | Math enthusiast | Mathematical art

If x = 1, y = - 1 and x = 3Y = - 5 are solutions of the equation AX + by + 2 = 0 about X and y, try to judge whether x = - 4 and y = 9 are solutions of the equation AX + by + 2 = 0?

Because: x = 1, y = - 1 for the solution of the equation AX + by + 2 = 0 of X and y, substitute x = 1, y = - 1 into the equation AX + by + 2 = 0
A-B + 2 = 0 (1)
Because: x = 3Y = - 5 is the solution of the equation AX + by + 2 = 0 about X and y, substituting x = 3Y = - 5 into the equation AX + by + 2 = 0
It is obtained that: - 5A - (5 / 3) B + 2 = 0 is reduced to: 15A + 5b-6 = 0 (2)
By solving the equations (1) (2), we get
a=-1/5
b=9/5
Substituting a and B into ax + by + 2 = 0, the equation - x + 9y + 10 = 0 (3) is obtained
Substituting x = - 4, y = 9 into equation (3)
-4+81+10 !=0
So x = - 4, y = 9 is not a solution of the equation AX + by + 2 = 0

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