Solve x + 3y + z = 1 2x – y – z = 6 5x + y + z = 1 (1, 6, 1) (1, 2, -6) (2, 1, -4) (-1, -2, 6)

Answer is (1, 2, -6)

x + 3y + z = 1   > first equation

2x – y – z = 6  > second equation

5x + y + z = 1 > third equation

Add second and third equation

2x – y – z = 6  > second equation

5x + y + z = 1 > third equation

7x = 7 (divide by 7 on both sides)

So x= 1

Now we add first and second equations

x + 3y + z = 1   > first equation

2x – y – z = 6  > second equation

3x +2y = 7

We already got x=1, replace it in the above equation

3(1) + 2y = 7

3 + 2y = 7 (subtract 3)

2y = 4 (divide both sides by 2)

So y =2

Now plug in the values in first equation

x + 3y + z = 1   > first equation

1 + 3(2) + z = 1

7 + z = 1 (subtract 7 from both sides)

z = -6

Answer is (1, 2, -6)

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