Question

The system below has the solution of (1,3) where A, B, C, D, E, and F are all nonzero real numbers.

Ax+By=C,Dx+Ey=F
Which of the following systems would not have (1,3) as the solution?

A. Ax+By=C and (2A-D)x+(2B+E)y=C-2F
B. Ax+By=C and 7Dx+7Ey=7F
C. Ax+By=C and (A+D)x+(B+E)y=C+F
D. (A/2+D)x+(B/2+E)y=(C/2+F).

Answer 1

To identify which system of equations would not have the solution (1,3), we substitute these values into the modified equations. We conclude that option D requires a closer look as it combines modified versions of both original equations, potentially altering the solution.

Step-by-step explanation:

We are given a system of linear equations with a known solution (1,3) and variables A, B, C, D, E, and F. To determine which system would not have (1,3) as the solution, we can substitute the values x = 1 and y = 3 into each system and see if both equations in the system are satisfied.

Analysis of Options

Option D is potentially concerning because it modifies both equations before combining them, which could change the validity of the solution (1,3). We should check this option more closely.