Answer: x = 7, y = -3, z = 1
Step-by-step explanation:
EQ 1: 3x + 4y - z = 8 solve for z
+z -8 +z - 8
3x + 4y - 8 = z
EQ 3: 5x + y - 2z = 30 substitute 3x + 4y - 8 for z and solve for x
5x + y - 2(3x + 4y - 8) = 30
5x + y - 6x - 8y + 16 = 30
-x - 7y + 16 = 30
-16 -16
-x - 7y = 14
+7y +7y
-x = 7y + 14
x = -7y - 14
EQ 2: x - 5y + 2z = 24 substitute 3x+4y - 8 for z and -7y - 14 for x
(-7y - 14) - 5y + 2(3x + 4y - 8) = 24
-7y - 14 - 5y + 6(-7y - 14) + 8y - 16 = 24
-7y - 14 - 5y - 42y - 84 + 8y - 16 = 24
-46y - 114 = 24
+114 +114
-46y = 138
÷-46 ÷-46
y = -3
x = -7y - 14
= -7(-3) - 14
= 21 - 14
= 7
z = 3x + 4y - 8
= 3(7) + 4(-3) - 8
= 21 - 12 - 8
= 1
