Simultaneous Equations By Elimination

In this video we are going to discover what simultaneous equations are, and how to solve them. Simultaneous equations are two or more equations with two or more unknowns. They are called simultaneous because they must be solved at the same time. If we plot the equations on the same graph, where they cross each other are the solutions. The answer to solving the equations simultaneously. There are 3 different methods we can use to solve simultaneous equations: plot them graphically and see where they cross each other, solve algebraically by elimination, solve algebraically by substitution. In this video we’ll look at the elimination method. Solving simultaneous equations by elimination only works when we have linear equations. Linear equations have an ‘x’ and a ‘y’, they cannot have any x-squareds or y-squareds. Start by lining the two equations up, one on top of the other with the x’s, y’s and numbers all lined up. We then need to eliminate either our x’s or our y's. Hence the method is called elimination! We need to have an equal number of one of those letters. We then eliminate the "matching" letter by either adding or subtracting the equations. If the signs are the same in front of the "matching" letters, we subtract. Just remember Same sign subtract - SSS. If the signs are different, we add the two equations. Adding or subtracting the two equations will eliminate one of the unknown letters. You can then easily solve for the other letter. With the solution, substitute this value back into one of the original equations to find a value for the letter than we eliminated. You will end up with a value for x and a corresponding value for y (x, y). This is the solution to these simultaneous equations. It is then really important to check your answers, so substitute (x, y) back into the other original equation.