X+y=33 4x+2y=120

You have a system of two linear equations with two variables:

1. x + y = 33
2. 4x + 2y = 120

To solve the system, we can use either the substitution method or the elimination method.

I'll demonstrate the elimination method:

First, we can manipulate the two equations so that when we subtract one from the other, one of the variables will be eliminated.

Let's double the first equation to be able to eliminate y:

2(x + y) = 2(33) 2x + 2y = 66

Now we have:

2x + 2y = 66 (3rd equation) 4x + 2y = 120 (given as the 2nd equation)

Now let's subtract the 3rd equation from the 2nd equation to eliminate y:

4x + 2y - (2x + 2y) = 120 - 66 4x + 2y - 2x - 2y = 120 - 66 4x - 2x = 120 - 66 2x = 54

Now, divide by 2 to find the value of x:

2x / 2 = 54 / 2 x = 27

Now that we have x, substitute it back into either equation to find y.

Using the first equation (x + y = 33):

27 + y = 33 y = 33 - 27 y = 6

Therefore, the solution to the system is x = 27 and y = 6.