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Question 54149: Solve the system for each variable:
y+z=6
x+5y-4Z=4
x-3y+5z=7
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! y+z=6
x+5y-4Z=4
x-3y+5z=7
:
Take the last two equations and eliminate x:
x + 5y - 4z = 4
x - 3y + 5z = 7
----------------subtract
0x +8y - 9z = -3
:
Using the 1st equation for substitution for y in 8y - 9z = -3:
y + z = 6
y = (6-z)
:
8(6-z) - 9z = -3
48 - 8z - 9z = - 3
-17z = -3 -48
-17z = -51
z = -51/-17
z = +3
:
:
Find y using the 1st equation, substituting 3 for z
y + z = 6
y + 3 = 6
y = 6 - 3
y = + 3 also
:
Find x using the 2nd equation, substituting 3 for y and z
x + 5y - 4z = 4
x +5(3) - 4(3) = 4
x + 15 - 12 = 4
x + 3 = 4
x = 4 - 3
x = +1
:
Check all three solutions in the 3rd equation:
x - 3y + 5z = 7
1 - 3(3) + 5(3) =
1 - 9 + 15 = 7; seems to be correct
:
Make sense to you??
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