Which of the following best describes the solution to the system of equations below?

Question

Which of the following best describes the solution to the system of equations below?

 

 

4x + 5y	=	7
12x + 15y	=	21

 

A. The system of equations has exactly one solution where x = 7/4 and y = 0.

B. The system of equations has no solution.

C. The system of equations has infinitely many solutions.

D. The system of equations has exactly one solution where x = 1 and y = 6/5.

Answer 1

If you look closely at the coefficients, you'll notice they are multiples of each other.  4x3 = 12 (for the x's)  and 5x3 = 15 (for the y's).  You should also notice that 7x3 = 21.  Since all values in the lower equation are the values of the upper equation multiplied by 3, these are actually the same equation for the same line.  Therefore, there are infinitely many solutions (C).