Algebra II Question?????????????

Question

Solve the system.

x+y-2z=5

x+2y+z=8

2x+3y-z=13

Is the answer IMS (infinitely many solutions) or is there an actual answer. I think it is IMS but I am not for sure.

Answer 1

x+y-2z=5......(1)

x+2y+z=8......(2)

2x+3y-z=13......(3)

(1)+(2): 2x+3y-z=13

So, essentially you only have two independent equations with three variables. Therefore, the answer is IMS.

Answer 2

Yes, you are correct!

If you take the first two equations and multiply the second by -1 and then add them together you get:

-y-3z=-3

Then take the second and third equation, multiply the second by -2 and then add them together you get:

-y-3z=-3

Obviously if you add these two you get zero, which means you have IMS to this system of equations.

Have a good day!