3x+y=20

8x-y=46
Use elimation

To solve the system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations.

Let's start by multiplying the first equation by 8 and the second equation by 3 to make the coefficients of y in both equations the same:

(8)(3x+y) = (8)(20)
(3)(8x-y) = (3)(46)

This simplifies to:

24x + 8y = 160
24x - 3y = 138

Now, we can subtract the second equation from the first equation:

(24x + 8y) - (24x - 3y) = 160 - 138
24x - 24x + 8y + 3y = 22
11y = 22

Divide both sides of the equation by 11 to solve for y:
y = 2

Plug this value back into one of the original equations to solve for x. Let's use the first equation:

3x + 2 = 20
3x = 18
x = 6

The solution to the system of equations is x = 6 and y = 2.