2х+у=11 3х-у=9

To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination.

First, multiply the first equation by 3 to make the coefficients of x in both equations equal:

3(2x + y) = 3(11) 6x + 3y = 33

Now, we have the system of equations: 6x + 3y = 33 3x - y = 9

Add the two equations together to eliminate y:

(6x + 3y) + (3x - y) = 33 + 9 6x + 3y + 3x - y = 42 9x + 2y = 42 ...(1)

Now, let's solve the second equation for y:

3x - y = 9 y = 3x - 9

Substitute y = 3x - 9 into equation (1):

9x + 2(3x - 9) = 42 9x + 6x - 18 = 42 15x - 18 = 42 15x = 42 + 18 15x = 60 x = 60/15 x = 4

Now, substitute the value of x back into either of the original equations. Let's use the first equation:

2x + y = 11 2(4) + y = 11 8 + y = 11 y = 11 - 8 y = 3

So, the solution to the system of equations is x = 4 and y = 3.