Take any point P on the triangle ABC, record the distances from P to three sides a, B, C as X, y, Z in turn, and prove that AZ + by + CZ is the fixed value

As shown in the figure above, link AP, BP and CP to divide △ ABC into three triangles
The areas of the three triangles are ax / 2, by / 2 and CZ / 2
So, the area of △ ABC is: (AX + by + CZ) / 2
Because the triangle has a certain area
So, no matter where point P is in the triangle ABC, ax + by + CZ is constant

1. Xiaoming and Xiaoyan solved the equations {ax + by = 16} at the same time. ① BX + ay = 1. ② Xiaoming copied the equation ① wrong and got the solution {x}
=-1y = 3 Xiaoyan copied equation 2 wrong, and the solution is {x = 3Y = 2, so we can find the solution of the original equations
2. When m is an integer, the solution of the equations is a positive integer? {2x my = 6 ① x-3y = 0 ②
3. A and B start at the same time from a and B, which are 60km apart. They run in opposite directions and meet each other in one hour. When they run in the same direction, a is in the back and B is in the front. After three hours, a can catch up with B. what are the speeds of a and B

On the system of x.y equations ax by = a; BX ay = B, where a ≠ B, then what is the solution of the system of x.y equations

ax-by=a (1)
bx-ay=b （2）
(1)×a-(2)×b
(a²-b²)x=a²-b²
therefore
If a + B = 0
Then x and y have innumerable solutions
a+b≠0
Then x = 1
y=(ax-a)/b=0

If the equations 5x + y = 13 x-2y = 7 and ax + by = 9 BX ay = - 7 have the same solution, find the values of a and B

5x+y=13①
x-2y=7②
From ① + ② * 2: 11x = 33
x=3
So x = 3
y=-2
So 3a-2b = 9
3b+2a=-7
The solution is: a = 1
b=-3
Give me some points

Take any point P on the triangle ABC, record the distances from P to three sides a, B, C as X, y, Z in turn, and prove that AZ + by + CZ is the fixed value