Math (linear algebra)
posted by ZUkii on .
Solve the system of equation.
x 2y+ 3z = 5
3x + y = 5
2x+y + z = 8

x 2y+ 3z = 5
3x + y = 5
2x+y + z = 8
First thing to check is that we have three equations and three unknowns, which is fine. If there are more unknowns than equations then there is a problem with the question.
x 2y+ 3z = 5
3x + y = 5
2x+y + z = 8
we need to eliminate one unknown by combining pairs of equations. Lets say we remove the y terms.
x 2y+ 3z = 5
3x + y = 5 (multiply by 2)
x 2y+ 3z = 5
6x + 2y = 10
Add these two and y terms are removed.
7x+3z=5
Do the same with, but this time subtract the two and the y terms are removed
3x + y = 5
2x+y + z = 8
5xz=13
We now have two equations and two unknwons
7x+3z=5
5xz=13 (multiply by 3)
7x+3z=5
15x3z=39
and add
22x=44, so x=2
substitute in here to find y
3x + y = 5
the substitute in one of the above to find z