Answer:
The values of the variables in the given linear system are:
x = 30
y = 18
z = 14
Explanation:
To find the value of y in the linear system, we can solve the system of equations:
x + y + z = 62
x - y = 12
2x + y + z = 92
We'll use the method of elimination to solve this system. We'll start by eliminating the y variable.
From equation 2), we can rewrite it as y = x - 12.
Now let's substitute this value of y in equations 1) and 3):
x + (x - 12) + z = 62
2x - 12 + z = 62
2x + z = 74 ----(4)
2x + (x - 12) + z = 92
3x - 12 + z = 92
3x + z = 104 ----(5)
Now we have a system of two equations with two variables (x and z). Let's solve this system.
Subtract equation (4) from equation (5):
(3x + z) - (2x + z) = 104 - 74
3x - 2x + z - z = 30
x = 30
Substituting the value of x back into equation (4):
2(30) + z = 74
60 + z = 74
z = 74 - 60
z = 14
Now we have the values of x and z. We can substitute these values into equation (2) to find y:
x - y = 12
30 - y = 12
-y = 12 - 30
-y = -18
y = 18
Therefore, the value of y in the given linear system is 18.