You can put this solution on YOUR website! Solve by substituting
x + y + z = 8
-3x + 2y + 4z = 8
2x + 5y + 3z = 16
:
Add the three equations, eliminate x
x + y + z = 8
-3x + 2y + 4z = 8
2x + 5y + 3z = 16
-------------------
0x + 8y + 8z = 32,
:
multiply 1st equation by 2 and subtract from the 3rd equation:
2x + 5y + 3z = 16
2x + 2y + 2z = 16
-------------------- eliminate x again
0x + 3y + z = 0
;
Two 2 unknown equations, now we can substitute
8y + 8z = 32
and
3y + z = 0
z = -3y
:
Substitute -3y for z in 8y + 8z = 32
8y + 8(-3y) = 32
8y - 24y = 32
-16y = 32
y =
y = -2
:
Substitute -2 for y in z = -3y
z = -3(-2)
z = 6
:
Substitute for y and z in the 1st equation and find x:
x - 2 + 6 = 8
x + 4 = 8
x = 8 - 4
x = 4
:
Check solution by substitution in the 2nd solution:
-3(4) + 2(-2) + 4(6) = 8
-12 - 4 + 24 = 8
