Question 164582This question is from textbook
: can someone please help me with this problem:
Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.
-2x + y + 4z = 10
-7x + 4y - 3z = 7
a. (19z - 33, 34z - 56, z)
b. (33 - 43z, 56 - 34z, z)
c. (-33 + 43z, 10 - 2x + 4z, z)
d. (-33 + 43z, 10 + 2x - 4z, z)
This question is from textbook
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
-2x + y + 4z = 10
-7x + 4y - 3z = 7
Leave only the x and y terms on the left:
-2x + y = -4z + 10
-7x + 4y = 3z + 7
Eliminate y by multiplying the first equation
by -4 and adding to the second:
8x - 4y = 16z - 40
-7x + 4y = 3z + 7
----------------------
x = 19z - 33
Eliminate x by multiplying the first equation
by -7 and the second by +2 and adding them:
14x - 7y = 28z - 70
-14x + 8y = 6z + 14
--------------------
y = 34z - 56
Therefore (x, y, z) = (19z-33, 34z-56, z) choice a
Edwin
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