Question

2m - 1 = n ;
3m - 1 = n
For the system of equations above, which of the following statement is true?

• A. There is only one (m, n) solution and n is negative.
• B. There is only one (m, n) solution and n is positive.
• C. There are infinitely many solution
• D. There are no solution to the system of equations.

Answer 1

The correct option is A There is only one (m, n) solution and n is negative.

Consider the ratio of coefficient of n's : $\frac{1}{1}$
Ratio of coefficient of m's : $\frac{2}{3}$
Since the ratio of coefficient of n's and m's are not equal. Therefore, the system will have a unique solution. Equate the LHS of the equations since RHS is n for both equations.
2m - 1 = 3m - 1
m = 0
Substitute in any equation, to get the value of n = -1.
Therefore, the correct answer is option A.