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

To solve this system of linear equations for x and y, we can use either substitution or elimination method. Here, the elimination method seems rather straightforward.

Let's start by arranging the equations:

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

We can make the coefficients of y in both equations equal so that we can eliminate y by subtracting the two equations. To do this, we could multiply the first equation by 2:

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

Now, we subtract this new equation from the second equation:

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

2x = 54

Now, we can solve for x:

2x = 54 x = 54 / 2 x = 27

Now that we have the value for x, we can substitute it back into the first equation to find the value for y:

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

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