How do i solve inequalitites with three variables. I still can't figure it outplease help.

x+y=1
y-z=-3
2x+3y+z=1

Where are the inequalities?
Those are equations.

Apologies for the confusion. It seems that you have a system of linear equations involving three variables, not inequalities. To solve this system of equations, we can use the method of substitution or the method of elimination to find the values of x, y, and z that satisfy all three equations simultaneously.

Let's use the method of substitution to solve this system.

Step 1: Choose one equation to solve for one variable in terms of the other two variables. Let's solve the first equation, x + y = 1, for x:
x = 1 - y

Step 2: Substitute the value of x in the other equations. Substituting x in equations 2 and 3, we get:
(1 - y) + y - z = -3 [Equation 2]
2(1 - y) + 3y + z = 1 [Equation 3]

Simplifying Equation 2:
1 - z = -3
z = 4

Simplifying Equation 3:
2 - 2y + 3y + z = 1
-2y + 3y + 4 = 1
y + 4 = 1
y = -3

Step 3: Substitute the values of y and z back into Equation 1 to find the value of x:
x + (-3) = 1
x = 4

Therefore, the solution to the system of equations is:
x = 4
y = -3
z = 4

To check the solution, substitute these values into all three equations and verify if they satisfy the given equations.