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In this method, we evaluate one of the variable value in terms of the other variable using one of the two equations.And that value is put into the second equation to solve for the two unknown values.
The solution below will make the idea of Substitution clear. x y = 15 -----(2) (10 y) y = 15 10 2y = 15 2y = 15 – 10 = 5 y = 5/2 Putting this value of y into any of the two equations will give us the value of x.
x y = 15 x 5/2 = 15 x = 15 – 5/2 x = 25/2 Hence (x , y) = (25/2, 5/2) is the solution to the given system of equations. 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.
You just have to follow the order for completing parts of the equation and keep your work organized to avoid mistakes!
In solving these equations, we use a simple Algebraic technique called "Substitution Method".
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.
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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. How much money does she need to buy a game that costs ?Solution: Let x represent the amount of money Jeanne needs.This article has over 222,861 views, and 14 testimonials from our readers, earning it our reader-approved status. The basic steps for solving algebra problems involve performing simple operations in small steps that “cancel” the original problem.Doing these steps carefully and in order should get you to the solution.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.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.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.So simple addition and subtraction will not lead to a simplified equation in only one variable.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.