Solve the system of equations: $$8x + 2y = 11$$ $$6x - 4y = 11$$

Solution:

We can solve this system of equations using the elimination method.

1. Multiply the first equation by 2 to make the coefficients of y opposites: $$2(8x + 2y) = 2(11) ightarrow 16x + 4y = 22$$
2. Add the modified first equation to the second equation: $$(16x + 4y) + (6x - 4y) = 22 + 11$$ $$22x = 33$$
3. Solve for x: $$x = \frac{33}{22} = \frac{3}{2}$$
4. Substitute the value of x back into the first equation: $$8(\frac{3}{2}) + 2y = 11$$ $$12 + 2y = 11$$ $$2y = 11 - 12$$ $$2y = -1$$ $$y = -\frac{1}{2}$$

Answer: $$x=\frac{3}{2}, y=-\frac{1}{2}$$