Question

Solve the following system of equations.

x + y – 4z = –7
2x + 3y – 3z = –6
2x + 2y – z = 0

Answer 1

Explanation:

- subtract 3rd from second

2x +3y -3z = -6

2x +2y -z = 0

---------------

0 y -2z = -6

- multiply first by -2 and assum by second

-2x -2y +8z = 14

2x +3y -3z = -6

----------------

0 y +5z = 8

y-2z=-6

y+5z=8

---------- subtract second from first

0 -7z =-14

z=2

y+5z=8

y+5*2=8

y+10=8

y=-2

z=2

y=-2

x+y -4z=-7

x +(-2) -4(2) = -7

x-2-8=-7

x-10=-7

x=3

x=3

y=-2

z=2

Answer 2

- subtract 3rd from second

2x +3y -3z = -6
2x +2y -z = 0
---------------
0 y -2z = -6

- multiply first by -2 and assum by second

-2x -2y +8z = 14
2x +3y -3z = -6
----------------
0 y +5z = 8

y-2z=-6
y+5z=8
---------- subtract second from first
0 -7z =-14
z=2

y+5z=8
y+5*2=8
y+10=8
y=-2

z=2
y=-2

x+y -4z=-7
x +(-2) -4(2) = -7
x-2-8=-7 x-10=-7
x=3

x=3
y=-2
z=2