Cho hệ phương trình: mx + y = 3m - 1; x + my = m + 1. a) Giải hệ phương trình khi m = - 3

a) Khi m = -3, ta có hệ phương trình:
-3x + y = 3(-3) - 1
x - 3y = -3 + 1

Simplifying the equations, we get:
-3x + y = -10
x - 3y = -2

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

Using the method of substitution:
From the second equation, we have x = 3y + 1.
Substituting this value into the first equation, we get:
-3(3y + 1) + y = -10
-9y - 3 + y = -10
-8y = -7
y = -7/-8
y = 7/8

Substituting the value of y back into the second equation, we get:
x - 3(7/8) = -2
x - 21/8 = -2
x = -2 + 21/8
x = -16/8 + 21/8
x = 5/8

Therefore, when m = -3, the solution to the system of equations is x = 5/8 and y = 7/8.

b) To find the value of m for the system of equations to have a unique solution (x, y) satisfying x = 3y + 1, we can substitute x = 3y + 1 into the first equation of the system:

mx + y = 3m - 1
m(3y + 1) + y = 3m - 1
3my + m + y = 3m - 1
(3m + 1)y + m = 3m - 1

For the system to have a unique solution, the coefficients of y in the equation above must be equal to 0. Therefore, we have:

3m + 1 = 0
m = -1/3

Therefore, the value of m for the system of equations to have a unique solution satisfying x = 3y + 1 is m = -1/3.