2x+y=9

8x-2y=6

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

1) Solve one equation for one variable in terms of the other variable.
2x + y = 9
y = 9 - 2x

2) Substitute this expression for y into the second equation.
8x - 2(9 - 2x) = 6

3) Simplify and solve for x.
8x - 18 + 4x = 6
12x - 18 = 6
12x = 24
x = 2

4) Substitute the value of x back into one of the original equations to solve for y.
2(2) + y = 9
4 + y = 9
y = 9 - 4
y = 5

The solution to the system of equations is x = 2 and y = 5.