Solve the two simultaneous equations: 2y + x = 8 [A] and 1 + y = 2x [B]

I have labelled the two separate equations A and B so that it is easier to talk about them. There are two ways in which you can do these equations but I am going to explain the method using substitution. As y and x are in both of the equations we can try to eliminate at least one of these unknowns for the moment. So, if we rearrange [B] so that y=2x-1 we can then substitute this value of y into [A]. This will give us: 2(2x-1) + x =8. By multiplying this out we get: 4x-2+x=8 By grouping the x values together: 5x-2=8 Then placing all the unknowns to one side of the equation 5x=10 and then dividing both sides by 5 we get: x=2. So we have found the value for x! We would then substitute this into [B]: 1+y=2(2),then multiplying this out 1+y=4, placing all the unknowns onto one side: y=3 So we have a solution for y! Just to check that our answers are correct we can substitute our two values into [A]: 2(3)+(2)=6+2 =8 and 8 is the correct answer so we know our solutions are correct!