Tìm m thỏa mãn

To solve the system of equations, we can use the method of substitution.

First, let's solve the first equation for x in terms of y:
mx - y = 1
mx = y + 1
x = (y + 1)/m

Now, substitute this expression for x in the second equation:
x + 4(m + 1)y = 4m
((y + 1)/m) + 4(m + 1)y = 4m

Multiply both sides of the equation by m to eliminate the fraction:
y + 1 + 4m(m + 1)y = 4m^2

Expand and simplify:
y + 1 + 4m^2y + 4my = 4m^2

Combine like terms:
(1 + 4m)y + 1 = 4m^2 - 1

Simplify further:
(1 + 4m)y = 4m^2 - 2

Divide both sides of the equation by (1 + 4m):
y = (4m^2 - 2)/(1 + 4m)

Now, substitute this value of y back into the expression for x:
x = (y + 1)/m
x = ((4m^2 - 2)/(1 + 4m) + 1)/m

Simplify further:
x = (4m^2 - 2 + 1 + 4m)/(m(1 + 4m))
x = (4m^2 + 4m - 1)/(m(1 + 4m))

Therefore, the solution to the system of equations is:
x = (4m^2 + 4m - 1)/(m(1 + 4m))
y = (4m^2 - 2)/(1 + 4m)