System of Equations 10 points

x+y-z = 1
2x+y-z = 4
x-2y+z = 0

Isolate x in the first equation:

x = -y + z + 1

Now substitute (-y + z + 1) for x in the equations below:

2(-y + z + 1) + y - z = 4
-y + z + 1 - 2y + z = 0

When expanded and simplified this gives:

-y + z = 2
-3y + 2z = -1

Now isolate z in the first equation:

z = y + 2

Now substitute (y + 2) for z in the second equation:

-3y + 2y + 4 = -1
-y = -5
y = 5

Now that you know what y equals, go back to one of the equations and solve for z:

-5 + z = 2
z = 7

Now that you know what both y and z equal, go back to one of the equations in the beginning and solve for x:

x + 5 - 7 = 1
x = 3
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Overall:

x = 3
y = 5
z = 7

As an ordered triple:

(3, 5, 7)

x+y-z = 1
2x+y-z = 4
x-2y+z = 0

Take 1 and 3 and eliminate z. Then take 2 and 3 and eliminate z also:

x+y-z = 1
x-2y+z = 0
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2x - y = 1 Eqn 4 ------>> y = 2x - 1
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2x+y-z = 4
x-2y+z = 0
======================================
3x - y = 4 Eqn 5 ------->> y = 3x - 4

=======================================…
Set right sides of 4 and 5 equal to each other and solve for x:

2x - 1 = 3x - 4

- 1 + 4 = 3x - 2x

3 = x Back substitute into 4 OR 5:

y = 2x - 1 = 2*3 - 1 = 6 - 1 = 5

Eqn 1: x+y-z = 1 ------->> z = x + y - 1

z = 3 + 5 - 1 = 8 - 1 = 7

(x, y, z) = (3, 5, 7)

Check in all three original equations.

Here ya go. Get rid of z by adding equa 1 And eq 3 tog: 2x -yis1. Or y is 2x-1
Ad. Eqn 2&3 tog: 3x - y is 4. Now substi for y:
3x - (2x-1). Is 4
X +1 is 4
X is 3

If x is 3, then. Y is 2x- 1 or y is 6-1 or 5 and
(Eqn 1) z is X+y-1
3+5-1
It checks out in all 3 eqn. luck!


:

x+y-z = 1
2x+y-z = 4
x-2y+z = 0

x=2y-z
2y-z+y-z=1
3y=1
y=1/3

x+(1/3)-z=1
x-(2/3)+z=0

x-z=2/3
x+z=2/3
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2x=4/3
x=2/3

z=0