Solve the system by substitution
-x-y-z= -8
-4x+4y+5z= 7
2x+2z= 4
2 answers:
Answer: x=3, y=6, z=-1
Step-by-step explanation:
2x+2z=4
2x=4-2z
X=2-z
-(2-z)-y-z=-8
-2+z-y-z=-8
-2-y=-8
-2+y=-8+y
-2+8=y
6=y
-4 (2-z)+4 (6)+5z=7
-8+4z+24+5z=7
9z=8-24+7
9z=-9
Z=-1
2x+2z=4
2x+2 (-1)=4
2x-2=4+2
2x=6
X=3
x=3 y=6 z=-1
- x - y - z = - 8 ------- (1) - 4x + 4y + 5z = 7 -------- (2) 2x + 2z = 4 --------- (3) From (3): x + z = 2 x = 2 - z --------- (4) Substitute (4) into (1), - x - y - z = - 8 - (2-z) - y - z = - 8 - 2 + z - y - z = -8 - 2 - y = - 8 2 + y = 8 Therefore, y = 6 Substitute y = 6 and (4) into (2), - 4x + 4y + 5z = 7 - 4(2 - z) + 4(6) + 5z = 7 - 8 + 4z + 24 + 5z = 7 9z + 16 = 7 9z = - 9 Therefore, z = - 9 Substitute z = - 9 into (4), x = 2 - z x = 2 - (-9) x = 2 + 9 Therefore x = 11 Solution: x = 11 y = 6 z = -9
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