# solving a hard problem

#### mattflint50

##### Junior Member
my teacher gave my class these three equations, and told us to solve for X,Y, and Z.

X+y+Z=4
2x-y+2Z=5
7X+y+7Z=22

I cant seem to find an answer. Ive tried to solve it algebretically, and by using crammer's rule, but it just wont come out. Is it even possible? Please help.

Thanx.

#### mattflint50

##### Junior Member
I understand what you just posted, but if im not mistaken, X,Y, and Z were not actually solved, because if you were to plug those numbers into the equations, it wouldn't come out how it was supposed to.

#### soroban

##### Elite Member
Hello, mattflint50!

pka's answer do work . . .

The equations are:
. . . . x + y + . z . = . .4
. . . 2x - .y + 2z . = . .5
. . . 7x + y + 7z . = . 22

He said: . x = r, .y = 1, .z = 3 - r
. . . Plug them in!

. . . . r + 1 + . (3 - r) . = . 4
. . . 2r .- 1 + 2(3 - r) . = . 5
. . . 7r + 1 + 7(3 - r) . = .22 . . . . They check out!

The system has an infinite number of solutions.

#### mattflint50

##### Junior Member
ok i see now, thank you