Question 1132289
2x + y - 2z = 10
 3x +2y + 2z = 1
 5x +4y + 3z = 4
:
Adding the 1st and 2nd equation
 3x +2y + 2z = 1
 2x + y - 2z = 10
------------------Addition eliminates z
5x + 3y = 11
:
Multiply the 1st equation by 3, multiply the 3rd equation and add
6x + 3y - 6z = 30
10x +8y + 6z =  8
---------------------addition eliminates z
16x + 11y = 38
:
Multipl 5x +3y = 11 by 16, multiply 16x + 11y = 38 by 5
80x + 48y = 176
80x + 55y = 190
----------------------Subtraction eliminates x, find y
0 - 7y = -14
y = -14/-7
y = + 2
:
Find x using 5x + 3y = 11
5x + 3(2) = 11
5x = 11 - 6
5x = 5
 x = 1
:
Find z using 2x + y - 2z = 10
2(1) + 2 - 2z = 10
-2z = 10 - 4
z = 6/-2
z = -3
;
;
Check solution in 3x + 2y + 2z = 1
3(1) + 2(2) + 2(-3) = 1
3 + 4 - 6 = 1