Answer:
Option (C).
Explanation:
The system of equations Mx + Ny = P ........... (1) and
Rx + Sy = T ........... (2) has a solution (1,3).
Now, in option (A),
The system of equations are Mx + Ny = P and 7Rx + 7Sy = 7T will also have a solution (1,3).
Because the first equation is the same as equation (1) and dividing both sides of the second equation will give the equation (2).
In option (B),
The system of equations are (M + R)x + (N + S)y = (P + T) and Rx + Sy = T will also have a solution (1,3).
Because, if we subtract the second equation from the first equation then we will get the equation (1) and the second equation itself is equation (2).
In option (D),
The system of equations are
and Rx + Sy = T will also have a solution (1,3).
Because multiplying the first equation with 2 will get the equation (1) and the second equation itself is equation (2).
In only option (C),
The system of equations are Mx + Ny = P and (2M - R)x + (2N - S)y = P - 2T will not have the solution (1,3).
This is because we can not obtain the equation (2) from the above two system of equations by any mathematical operation.
Hence, option (C) will be the answer.