In Exercises 23-36, solve the system using either Gaussian elimina - tion with back-substitution or Gauss-Jordan elimination. 23. x + 2y = 7 2x + y = 8 25. - x + 2y = 1.5 2x - 4y = 3

23) x = 3, y = 4

24) Any (x, y) values where x = 1.5 - 2y

Step-by-step explanation:

For the first system (23), it goes like this

[1 2 | 7]

[2 1 | 8]

We need to do L2 = L2 - 2L1, so now it is

[1 2 | 7]

[0 - 3 |-6]

So, now we have:

-3y = - 6 * (-1)

3y = 6

y = 2

x + 2y = 7

x + 4 = 7

x = 3

Now for system 24, we have:

[-1 2 | 1.5]

[2 - 4| 3]

We do L2 = L2 + 2L1, so we have:

[-1 2 | 1.5]

[0 0| 0]

So there are infinite solutions for this system. The solution for this system will be each (x, y) pair where x = 1.5 - 2y.