Final answer:
The value of x+y in the given system of equations is 300.
Step-by-step explanation:
To find the value of x+y in the system of equations x+y+3z=600 and x+y+z=400, we can solve for x and y separately and then add them together.
First, subtract the second equation from the first equation to eliminate z:
x+y+3z - (x+y+z) = 600 - 400
2z = 200
z = 100
Substitute the value of z back into the second equation and solve for x+y:
x+y+100 = 400
x+y = 400 - 100
x+y = 300
Therefore, the value of x+y is 300.