Solve the simultaneous equations x+y=8 and 3x-y=4.

Notice that y has the same coefficient (ignoring the sign) in both equations. So, we will use the elimination method. The elimination method means that we will combine the two equations to eliminate the y variable, allowing us to find the value of x. Then, we will substitute this value of x in order to find y.Since y has opposite signs in the two equations, we will eliminate y by adding the equations. Adding gives (x+y) + (3x-y) = 8 + 4. Simplifying gives us 4x = 12 so x = 3. Now, by substituting x = 3 into x + y = 8 we get that 3 + y = 8 so y = 5. Hence we have solved our simultaneous equations and have that x = 3 and y = 5.