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Question 189199: Solve each of these system of equations.
1) x + 2y + z = 10
2x - y + 3z = -5
2x - 3y - 5z = 27
a) x = 4, y = 7, z = -5
b) x = -5, y = 4, z =7
c) x = 7, y = -5, z = 4
d) x = 7, y = 4, z = -5
On this question use the RREF function on your calculator
2) 3x + y + z = 4
2x + 2y + 3z = 3
x + 3y + 2z = 5
a) x = -1, y = 2, z = 1
b) x = 2, y = 1, z = -1
c) x = 1, y = 2, z = -1
d) x = 1, y = -1, z = 2
May you explain how to solve these questions?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve each of these system of equations.
1) x + 2y + z = 10
2x - y + 3z = -5
2x - 3y - 5z = 27
a) x = 4, y = 7, z = -5
b) x = -5, y = 4, z =7
c) x = 7, y = -5, z = 4
d) x = 7, y = 4, z = -5
--------------------
x + 2y + z = 10
2x - y + 3z = -5
2x - 3y - 5z = 27
There's more than one way to do these. If you get one on a timed test, and you have 4 solutions to choose from, as in this one, sub the values in to find which of the 4 it is. That's quicker by far, IF you don't have to show your work for the test.
Then there's elimination and substitution. You pick one of the 3 variables and eliminate it from 2 of the equations. x is as good as any for this problem.
Multiply by whatever is needed to get the same coeffs for all 3 eqns, in this case eqn 1 times 2 will do it.
x + 2y + z = 10 -->
2x + 4y + 2z = 20
2x - y + 3z = -5
2x - 3y - 5z = 27
Then subtract one eqn, the 3rd, from the 1st and the 2nd.
2x + 4y + 2z = 20
2x - 3y - 5z = 27
----------------- Subtract
0x + 7y + 7z = -7 eqn A
--------------
2x - y + 3z = -5
2x - 3y - 5z = 27
----------------- Subtract
0x + 2y + 8z = -32 eqn B
Now there are 2 eqns in 2 variables, A and B.
Multiply again to get the same coeffs
y + z = -1
y + 4z = -16
------------ Subtract
0y -3z = 15
z = -5 zzzzzzzzzzzzzzzzzzzzzzzzzzzz
------------
y + z = -1
y = 4 yyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
------------
x + 2y + z = 10
x = 7 xxxxxxxxxxxxxxxxxxxxxxxxxxxx
That's answer d.
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Another method is determinants. I made an Excel sheet that does these up to 4 by 4.
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I don't have a calculator that does these.
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