System of equation help please. I'm really lost. Help!!?

Question

2x-5y+z=5
3x+2y-z=17
4x-3y+2z=17

how would I solve this? Can sumone help me?

Answer 1

you would solve this by combining the equations in order to remove some of the variables.
here's a hint for the first step.
notice the first and third equations. if you multiply the first eq by 2, you get
4x-10y+2z=10.
if you then subtract the third equation from that, the x's and z's go to zero. so you can then solve and get a numerical value for y.
plug back into the system and you can move on from there.
Hope that helps without just doing the work for you.

Answer 2

if we add together the first 2 equations we get
2x-5y+z+3x+2y-z=5+17
let's rewrite that
2x+3x-5y+2y+z-z=22
let's do the elementary sums
5x-3y=22
you see I removed the z so the equation became simpler
Not lets try again using the second and third equations
I multiply the second equation by 2
2*3x+2*2y-2z=2*17
I do the multiplication
6x+4y-2z=34
And I sum that with the third equation
6x+4y-2z+4x-3y+2z=34+17
I do some clean up and get
10x-y=51
but remember we already got 5x-3y=22
if I multiply 5x-3y=22 by -2 I get
-10x+6y=-44
that I sum with 10x-y=51 to get
-10x+6y+10x-y=-44+51
hence
5y=7
or y=7/5
you can now replace y by 7/5 in 5x-3y=22 to get x
and replace x and y by their values in any equation to get z