Solve the simultaneous equations: 2x + y = 18 and x - y = 6

Note the following rules for simultaneous equations: 'Same sign subtract' and 'alternate sign add'. The first thing we need to do is find either y or x. To do so here, you add the equations together because the signs are different. 2x + y + x - y = 18 + 6 which becomes 3x = 24. To find x you have to divide both sides by 3, which gives you x = 8. The next step is to find y, you do this by placing the value of x into one of the equations which gives you 8 - y = 6. You then solve this equation to find y, 8 - y = 6. Add y to both sides to eliminate the negative to get 8 = 6 + y. Minus 6 from both sides to find y which gives you y = 2. You now know that x = 8 and y = 2 (but just to check this I like to insert both numbers into the other equation to make sure I have the right values: (2 x 8) + 2 = 18 which gives you 18 = 18 and shows that you are correct.