Question

The system Mx+Ny=P has the solution (1,3), where Rx+Sy=T

M,N,P,R,S and T are non zero real numbers. Which of the following system would not have (1,3) as a solution.

Answer 1

The answer is definitely C. My friend took the test and got it correct.

Answer 2

Given:

The system Mx+Ny=P has a solution (1,3) where Rx+Sy=T; M, N, P, R,S and T are non-zero real numbers.

Solve for M, N, R, P, S, T:

M +3N = P
R + 3S = T

The given choices should simplify to the equations above.

A) Mx +Ny = P
7Rx + 7Sy = 7T
7(Rx + Sy) = 7T
Rx + Sy = T
remarks: CORRECT

B) (M+R)x + (N+S)y = P + T
Rx + Sy = T
Mx + Rx + Ny + Sy = P + T
Mx + Ny + T = P + T
Mx + Ny = P
remarks: CORRECT

C) Mx + Ny = P
(2M - R)x + (2N - S)y = P - 2T
2Mx - Rx + 2Ny - Sy = P - 2T
2(Mx + Ny) - (Rx + Sy) = P - 2T
2P - (Rx + Sy) = P - 2T
remarks: INCORRECT