Question

One more question. Can you please show the steps of how to solve this. I feel like the way I'm solving this is wrong.

Solve for x y and z
X+5y+3z=7
2x+y+4z=1
2x-y+2z=1

Answer 1

Not knowing how your are solving it, I would go to matrix methods on your calculator.

1,5,3,7
2,1,4,1
2,-1,2,1
http://www.mathportal.org/calculators/system-of-equations-solver/system-3x3.php

Answer 2

hard to say, since you don't show your work. One way is substitution.

x = 7-5y-3z, so using that in the last two equations, you get

2(7-5y-3z)+y+4z = 1
2(7-5y-3z)-y+2z = 1
shuffling things about, that gives
9y+2z = 13
11y+4z = 13
Now, since 2z = 13-9y, use that to get
11y+2(13-9y) = 13
7y = 13
y = 13/7
2z = 13-9y, so z = -13/7
x = 7-5y-3z = 23/7

Or, using elimination,
subtract 2*#1 from #2 and #3:
1x+5y+3z = 7
0x-9y-2z = -13
0x-11y-4z = = -13

add 5*#2 to 9*#1
subtract 11*#2 from 9*#3

1x+0y+17z = -2
0x-9y-2z = -13
0x+0y-14z = 26

Now you can see that z = -13/7
and use that to get y, then x.