x+2y+z= 4   5x-y-z=1    3x+y+3z=17  solve x, y and z

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x+2y+z= 4.....(1)

5x-y-z=1 .....(2)

3x+y + 3z=17....(3)

We are going to use the elimination method t solve the system:

Let us first add (2) and (3)

==> 8x + 2z = 18 .....(4)

Now let us multiply (2) by 2 and add to (1)

==> 10x-2y-2z=2

        x+2y+z=4

==> 11x...

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x+2y+z= 4.....(1)

5x-y-z=1 .....(2)

3x+y + 3z=17....(3)

We are going to use the elimination method t solve the system:

Let us first add (2) and (3)

==> 8x + 2z = 18 .....(4)

Now let us multiply (2) by 2 and add to (1)

==> 10x-2y-2z=2

        x+2y+z=4

==> 11x -z = 6 . ==> z= 11x-6

Now substitute z in (4)

8x+2z =18

8x+ 2(11x-6) = 18

8x +22x -12= 18

30 x = 30

=> x= 1

==> z= 11x-6 = 11(1)-6= 5

==> y = 5x-z-1= 5(1) - 5 -1 = -1

 

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