Question

Construct a consistent and independent system of equations that has (-1,7) as its solution. use x and y as your variables, and put your equations in the form Ax+By=C with A≠0 and B≠0 a) 2x - 3y = 11

b) 4x + y = 3
c) -5x + 2y = -17
d) 3x + 7y = 20

Answer 1

A consistent and independent system of equations that has (-1,7) as its solution can be constructed using the equations 2x - 3y = 11 and 4x + y = 3.

Step-by-step explanation:

A consistent and independent system of equations that has (-1,7) as its solution can be constructed using the equations 2x - 3y = 11 and 4x + y = 3.

To check if the system is consistent, substitute the values of x and y from the given solution (-1,7) into both equations:

1. For the first equation, substitute x = -1 and y = 7:
   2(-1) - 3(7) = 11
   -2 - 21 = 11
   -23 = 11. Since the left side does not equal the right side, the system is not consistent.
2. For the second equation, substitute x = -1 and y = 7:
   4(-1) + 7 = 3
   -4 + 7 = 3
   3 = 3. Since the left side equals the right side, the system is consistent.

Therefore, the system of equations 2x - 3y = 11 and 4x + y = 3 is consistent and has (-1,7) as its solution.