Nate T. answered • 02/14/20
Electrical Engineer with Experience Tutoring Math and Physics
x + 2y − 2z = 0
3x + 5y − 3z = 20
-4x − 3y + z = -28
The elimination method starts out by picking a variable to eliminate. I'll pick x.
Let's start with the first two equations. We need to figure out what to multiply the first equation by so that when we add the two equations together, the x's cancel out. That number is -3, as shown below:
-3*(x + 2y − 2z) = 0*-3
- 3x - 6y +6z = 0 We then add this to the second equations:
- 3x - 6y +6z = 0
3x + 5y − 3z = 20
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0x -1y + 3z = 20 -> -y + 3z =20
Next we do the same thing with equations 1 and 3. This time we'll multiply equation 1 by 4.
4x + 8y − 8z = 0
-4x − 3y + z = -28
------------------------
0x + 5y - 7z = -28 -> 5y - 7z = -28
We have now created two equations with two unknowns. We will use elimination again to get rid of the y's:
-y + 3z =20
5y - 7z = -28
multiply the top equation by 5:
-5y + 15z = 100
5y - 7z = -28
--------------------
8z = 72
z = 9
We have our first answer! now we can plug that back into our top equation:
-y + 3*9 = 20
-y = -7
y = 7
We now have two answers! We can plug both of those back into one of our original equations to solve for x. I'll do the 1st equation:
x + 2*7 − 2*9 = 0
x = 18 - 14
x = 4
So your answer is (x,y,z) = (4,7,9)
I hope that cleared things up for you! If not, let me know.
