Solve the following system of equations carefully show how you arrive to your answer

Question

4x+2y-z=21

-x-2y+2z=13

3x-2y+5z=70

Answer 1

A 4x+2y -z=21

B -x-2y+2z=13

C 3x-2y+5z=70

to eliminate y

Add A+B 3x + 4z = 154

Add A+C 5x + 4z = 91

Subtrace A+C from A+B 12x + 4z = 616

-5x - 4z = 91

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7x = 525

x = 75

3x + z = 154

3·75 + z = 154

225 + z = 154

z = -71

A 4·75 + 2y + 71 = 21

2y = -350

y = -175

Answer 2

Elimination method could be used to solve this system of linear equations.

Step 1. Adding 1st and 2nd equations results in 3x+z=34, which could be written as 9x+3z=102;

Step 2. Subtracting 2nd from 3rd equations results in 4x+3z=57; subtracting it from the equation shown above results in 5x=45, or x=9.

Step 3. Plug the value of x into the equation above (i.e. 3x+z=34) to get: 27+z=34, or z=7;

Step 4. Finally, 36+2y-7=21, which gives the answer for y=-4;

Therefore, x=9, y=-4 and z=7 (final answer)