Question 15516
Solve the system of linear equations:

{{{x - 4y = 2}}}
{{{x + 2y = 8}}} Subtract the first equation from the second equation, eliminating the x term and resulting in:

{{{6y = 6}}} Divide both sides by 6.
{{{y = 1}}} Now substitute this value of y into either of the two original equations and solve for x. Let's use the first equation.

{{{x - 4(1) = 2}}} Add 4 to both sides.
{{{x = 6}}}

Solution is: (6, 1)

You can check this solution by substituting the x and y (6, 1) of the solution into the two equations and see that they are valid. 
I'll leave this as an exercise for you.