How do you solve the system 3x + z = 13, 2y + z = 10, x + y = 1?

1 Answer
Nov 21, 2015

x=1
y=0
z=10

Explanation:

Write all the equations

3*x + z = 13 equation 1
2*y + z = 10 equation 2
x + y =1 equation 3

The goal is to have at least one equation with only x, y or z

We subtract equation 1 with equation 2 we get:

3*x + z -(2*y + z) = 13-10 (equation 1- equation 2)
3*x - 2*y = 3 (equation 1- equation 2)

Add equation 3 two times

3*x - 2*y + 2*(x+y)= 3 + 2*1
5*x =5
x = 1

x + y = 1 equation 3
y=1-x=1-1=0
y=0

2*y+z=10
2*0+z=10
z=10

Check so that this works with the equation system,