Solve the following simultaneous equations: 2y+x=8 , 1+y=2x

This is a very common type of question that might be asked in an exam and there are 3 methods we could use to solve this; by substitution, by elimination (or subtraction) or by using straight line graphs. The elimination method involves taking one equation away from the other to cancel away one of the unknowns (x or y) and the straight line graph method lets you find the solution as a coordinate where the two lines intersect when plotted. For this specific question, I will use the substitution method as it is the easiest: 1) Label the equations, so we get 2y+x=8 is {1} and 1+y=2x is {2}. 2) Rearrange {2} so that y is the subject of the equation and label this as {3}, i.e. y=2x-1 {3}. 3) Substitute {3} into {1} and solve for x, i.e. 2(2x-1)+x=8 which gives 5x=10 so x=2. 4) Substitue this value of x into the equation {3} and solve for y, i.e. y=22–1 which gives y=5. 5) Check these values for x and y are correct by substitutaing them into one of the original equations, i.e. equation {2} reads 1+5 = 23. Since 1+5 = 2*3 = 6, we know we have found the correct values for x and y.