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Examples given next are similar to those presented above and have been shown in a way that is more understandable for kids.If we use the method of addition in solving these two equations, we can see that what we get is a simplified equation in one variable, as shown below.2x y = 15 ------(1) 3x – y = 10 ------(2) ______________ 5x = 25 (Since y and –y cancel out each other) What we are left with is a simplified equation in x alone.
2x – y = 10 ------(1) 2x – 4 = 10 2x = 10 4 = 14 x = 14/2 = 7 Hence (x , y) =( 7, 4) gives the complete solution to these two equations.
In Algebra, sometimes you may come across equations of the form Ax B = Cx D where x is the variable of the equation, and A, B, C, D are coefficient values (can be both positive and negative). S (Right Hand Side) gives x = 11 Hence x = 11 is the required solution to the above equation.
However, we can multiply a whole equation with a coefficient (say we multiply equation (2) with 2) to equate the coefficients of either of the two variables.
After multiplication, we get 2x 4y = 30 ------(2)' Next we subtract this equation (2)’ from equation (1) 2x – y = 10 2x 4y = 30 –5y = –20 y = 4 Putting this value of y into equation (1) will give us the correct value of x.
So if we add the two equations, the –y and the y will cancel each other giving as an equation in only x. x – y = 10 x y = 15 2x = 25 x = 25/2 Putting the value of x into any of the two equations will give y = 5/2 Hence (x , y) = (25/2, 5/2) is the solution to the given system of equations.
Elimination Method - By Equating Coefficients: In Elimination Method, our aim is to "eliminate" one variable by making the coefficients of that variable equal and then adding/subtracting the two equations, depending on the case.Doing the Sometimes you have to use more than one step to solve the equation.In most cases, do the addition or subtraction step first.Of course we have not been looking to prove this in the first place!!Hence we conclude that there is no point in substituting the computed value into the same equation that was used for its computation. As shown in the above example, we compute the variable value from one equation and substitute it into the other.When solving a simple equation, think of the equation as a balance, with the equals sign (=) being the fulcrum or center.Thus, if you do something to one side of the equation, you must do the same thing to the other side.There will be no change in the equation solving strategy and once you have learnt the above method, you do not need to bother about the coefficients at all.Next we present and try to solve the examples in a more detailed step-by-step approach.This is another very easy and useful equation solving technique that is extensively used in Algebraic calculations. In this example, we see that neither the coefficients of x nor those of y are equal in the two equations.So simple addition and subtraction will not lead to a simplified equation in only one variable.