Solve the following simultaneous equations: 3x + y = 11, 2x + y = 8

This problem can be solved by using elimination.Label 3x + y = 11 as equation (1) and 2x + y = 8 as equation (2).We first want to eliminate one of the variables so that we can then reach a value for the other variable. To eliminate a variable, the coefficient of that variable in both equations need to be the same. If they are, we can add or subtract the equations from each other to eliminate the variable. In this example, in both equations, the coefficient of ‘y’ is 1. This means that y can be eliminated by subtracting equation (2) from equation (1).This leaves us with a new equation (3) which is (3-2)x + (1-1)y = (11-8) or in other words 1x + 0y = 3 which becomes x = 3. From this we can see that we now have our value for x which is x = 3.Now that we have a value for one variable, we can use it to calculate the value for the other variable (the eliminated variable), in this example, y. This can be done by using substitution. Using our value from equation (3), we can substitute this into either of the original equations and then solve to find the other variable. In our problem, we can do this by substituting x = 3 into equation (1). This gives us 3(3) + y = 11 which is the same as 9 + y = 11. All there is left to do now is rearrange to make y the subject and solve. We can do this by subtracting 9 from both sides, leaving us with y = 11 - 9, or y = 2, so giving us our value for y.Our final answer is therefore x = 3 and y = 2. These values can be checked by substituting them back into either of the original equations and checking the answers is consistent. For example, if we substitute back into equation (2), we get 2(3) + (2) = 8 which leaves us with 8 = 8, so therefore, our answers are correct.