Determine the number of solutions of this system of linear equations:%0D%0A%0D%0A−x+y=3%0D%0A−%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A3%0D%0A %0D%0A%0D%0A−2x+2y=3

Answer 1

To determine the number of solutions, we need to check if the two lines represented by these equations are parallel, coincident, or intersecting.

The given system of equations is:
1. −x + y = 3
2. −2x + 2y = 3

Let's rewrite equation 2 by dividing both sides by 2:
2'. -x + y = 1.5

Comparing equations 1 and 2', it can be seen that the two equations are different but they also have a proportional relationship. This means they represent parallel lines and do not intersect.

Therefore, this system of equations has no solutions.