Solve the system by elimination:
2x - y + 5z = 28
2x - 10y - 5z = 6
x + 5y - 4z = -23
2x - y + 5z = 28 (1)
2x - 10y - 5z = 6 (2)
x + 5y - 4z = -23 (3)
Multiply first equation by -10
-20x + 10y - 50z = -280
Add this to (2) and we get
-18x - 55z = -274 (4)
Multiply the last equation by 2
2x + 10y - 8z = -46 (5)
Add this to(2) and we get
4x -13z = -40 (5)
Using (4) and (5)
-18x - 55z = -274 multiply by 4
4x - 13z = -40 multiply by 18
-72x - 220z = -1096
72x -234 z = -720 add these
- 454z = 1816 divide both sides by -454
z = 4
And
4x - 13(4) = -40
4x -52 = -40
4x = 52-40
4x = 12
x = 3
And
2(3) - y + 5(4) = 28
12-y + 20 = 28
32 - y = 28
y = 4
{ x, y, z} = { 3, 4, 4}