Question

"How could you change this system so that it has no solution?

-x + y = -4
-x + 2y = -10
Write your new system AND explain why it is inconsistent."

Answer 1

To create an inconsistent system from -x + y = -4 and -x + 2y = -10, one could multiply the second equation by 2 to get -2x + 4y = -20. These equations are now parallel and do not have a solution because they will never intersect.

Step-by-step explanation:

To change the system so that it has no solution, we need to make the system inconsistent. The system given is:

• -x + y = -4
• -x + 2y = -10

We can change the coefficients of the variables in one of the equations while keeping the other the same so that the equations are parallel. For example, multiply the second equation by a scalar that does not change y's coefficient. Let's multiply the entire equation by 2:

• -x + y = -4
• -2x + 4y = -20

The new system has the equations:

• -x + y = -4
• -2x + 4y = -20

These two equations are inconsistent because they represent two lines that are parallel and will never intersect, meaning there is no pair (x, y) that solves both equations simultaneously.