solve the following system of equations

Question

5x-y+z=6

4x+2y-3z=14

x-3y+2z=-12

Answer 1

We can solve this system by first eliminating z from the second and third equations, (B) and (C).  Multiply the first equation, (A) by 3 and add it to (B), and multiply (A) by -2 and add it to (C):

 

15x - 3y + 3z = 18

4x + 2y - 3z = 14

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19x -y          = 32 (D)

 

-10x + 2y - 2z = -12

x - 3y + 2z = -12

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-9x - y = -24 (E)

 

multiply (E) by -1 and add it to (D):

 

19x - y = 32

9x + y = 24

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28x = 56  ==> x = 2

 

Now use the answer for x in (E):

 

9*(2) + y = 24 ==> y = 6

 

Use this in (A):

 

5*(2) - (6) + z = 6  ==> z = 2

 

Check that (x=2, y=6, z=2) is correct by plugging these values into (B) and (C):

 

4*(2) + 2*(6) - 3*(2) = 14  correct

 

(2) - 3*(6) + 2*(2) = -12  correct