A and B solve the equations ax + by = 2, mx-7y-8 = 0 A solution to x = 3, y = - 2, B bar m wrong, solution to x = - 2, y = 2, find a. B, M

A and B solve the equations ax + by = 2, mx-7y-8 = 0 A solution to x = 3, y = - 2, B bar m wrong, solution to x = - 2, y = 2, find a. B, M

Take x = 3, y = - 2, x = - 2, y = 2 into ax + by = 2
3a-2b=2
-2a+2b=2
∴a=4 b=5
∴4x+5y=2
Substituting x = 3, y = - 2 and mx-7y-8 = 0, we get
3m+14-8=0
∴m=-2

A and B solve the system of equations about X. y, ax + by = 2, mx-7y = 8. A correctly solves and finds the solution as x = 3, y = 2. B gets x = - 2, y = - 2 because of the wrong copy of M
Finding a, B, M

Substituting the correct solution x = 3, y = 2, 3A + 2B = 2, ①, 3m-14 = 8,
The result is: M = 22 / 3
B copy error m, no copy error a, B, substitute x = - 2, y = - 2 into ax + by = 2, get: - 2a-2b = 2, ②
① A = 4,
Substituting a = 4 into (1) gives B = - 5
So, a = 4, B = - 5, M = 22 / 3

A and B solve the system of equations ax + by = 2, mx-7y-8 = 0, a right solution to x = 3, y = 2, (note that 2) B wrote m wrong, solve x = - 2, y = - 2, find a, B, M

Solution: substitute x = 3, y = 2 into the equation: mx-7y-8 = 0, get: 3m-14-8 = 0, M = 22 / 3. Substitute x = 3, y = 2 into the equation: ax + by = 2, get: 3A + 2B = 2. - (1) substitute x = - 2, y = - 2 into the equation: ax + by = 2, get - 2a-2b = 2. - (2) substitute (1), (2) simultaneous equations, get: a = 4, B = - 5