Answer:
x= 3, y=0, z= 1
Explanation:
Let's label the 3 given equations first.
2x +3y +4z= 10 -----(1)
3x +2y -4z= 5 -----(2)
x +4y +2z= 5 -----(3)
(1) +(2):
This is to eliminate the z term.
2x +3y +4z +3x +2y -4z= 10 +5
5x +5y= 15
Divide by 5 on both sides:
x +y= 3 -----(4)
(3) ×2:
2x +8y +4z= 10 -----(5)
(2) +(5):
This is to eliminate z term.
3x +2y -4z + 2x +8y +4z= 5 +10
5x +10y= 15
Divide by 5 throughout.
x +2y= 3 -----(6)
(6) -(4):
x +2y -(x +y)= 3 -3
x +2y -x -y= 0
y= 0
subst. y=0 into (4):
x +0= 3
x= 3
subst. x=3, y=0 into (3):
3 +4(0) +2z= 5
3 +2z= 5
2z= 5 -3
2z= 2
z= 2÷2
z= 1