Question

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

Answer 1

Answer:

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.