SOLUTION: solve 2x - 3y - 3z = 2 x + 5y + 2z = -3 x + 2y = 0 thank you

Question 65799This question is from textbook An Incremental Development
: solve
2x - 3y - 3z = 2
x + 5y + 2z = -3
x + 2y = 0
thank you This question is from textbook An Incremental Development

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
solve
Eq 1: 2x - 3y - 3z = 2
Eq 2: x + 5y + 2z = -3
Eq 3: x + 2y = 0
:
It's quite easy to get this to a "two equation two unknown" situation using Eq 3.
:
x + 2y = 0
x = -2y
Substitute -2y for x in eq 1 and 2
2(-2y) - 3y - 3z = 2
-4y - 3y - 3z = 2
-7y - 3z = 2
and
-2y + 5y + 2z = -3
3y + 2z = -3
:
Mult -7y + 3z = 2 by 2 and 3y + 2z =-3 by 3 and you have:
:
-14y - 6z = 4
9y + 6z = -9
----------------adding eliminates z, solve for y
-5y + 0 = -5
y = -5/-5
y = +1
:
Use equation 3 to find x
x + 2y + 0
x + 2(1) = 0
x = -2
:
Substitute for x and in equation 1 and find z
2x - 3y - 3z = 2
2(-2) - 3(1)- 3z = 2
-4 - 3(1) - 3z = 2
-7 - 3z = 2
-3z = 2+7
z = 9/-3
z = -3
:
Check our solutions in the 2nd equation:
x + 5y + 2z = -3
-2 + 5(1) + 2(-3) = -3
-2 + 5 - 6 = -3 proves our solutions

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