Question

The sum of three numbers is 7. One of the numbers is one more than the sum of the other two numbers. It is also four times the difference between the two numbers.

Alright, this is how I interpreted it:

x + y + z = 7
x + y + 1 = z
4 (x-y) = z

I get the feeling I did something wrong already.
Moving on.

x + y - z = -1
4x - 4y -z = 0

I figured this is how the matrix will look like:

1 1 1
1 1 -1
4 -4 -1

then I multiplied its inverse by this

7
-1
0

And got 2, 0.4 and 8.5. I'm sure it's not the right answer so what am I doing wrong?

Answer 1

you can rref it on a TI 83

Answer 2

Is it x=2 y=1 z=4 ?

Answer 3

Oh yes, I am sure.

Answer 4

???

Answer 5

oh you're asking me lol

Answer 6

that was the correct answer but I have no idea why

Answer 7

try to solve the answer more easily......look x+y=z-1 and x+y+z=7 so z-1+z=7.solve it and get z=4. then x-y=x/4 and z=4 so x-y=1. From x+y=z-1,x+y=3.Now it is easy to solve x-y=1 & x+y=3 which is x=2 and y=1

Answer 8

thanks for the answer. I'm still not sure about the process but it's ok :)