The Substitution Method The Substitution Method If we have two linear equations in the form of two unknown variables x and y are said to be in form of a system of simultaneous linear equations if each of them is satisfied by the same pair of values of the variables x and y. So we call it as the solution of the pair of the linear equations. Linear pair of equations can be solved by different ways. When we talk about the algebraic method of solving the linear equations, we come across different methods namely elimination method, substitution and by cross multiplication methods. Any of these methods can be used to get the solution of the pair of linear equations in two variables. Now we will understand Substitution Method. By Substitution Method we mean that one of the variable in the pair of two equations are eliminated and then the second equation is also written in the form of one variable equation by the method of substitution. Let us look at the steps to be followed to perform the substitution method of solving the pair of linear equations: Suppose we are given two linear equations in the two variables form i.e. x and y. Now if we need to solve this pair of equations by the substitution method, we will follow the following steps: Step 1 : express y in the terms of x in one of the two given equations. Step 2 : Substitute this value of y in terms of x in the another equation. This helps us to get the linear equation in the form of one variable x. Know More About :- Quadratic Equation Application
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Step 3 : Now we will solve the linear equation in form of x which we have received in step 2 and thus get the value of x variable . Step 4 : Now we substitute the value of x in the relation which has both the variables x and y and it helps us to attain the value of y in the linear equation. Step 5 : We solve the above linear equation in y to get the value of the variable y. Let us consider the following pair of equations and solve them by the Substitution Method. 2x + y = 7 4x – 3y + 1 = 0 Sol: we can write the above equations as follows: 2x + y = 7 ------ ( 1) And 4x – 3y = -1 -----(2) (1) Equation can also be written as y = 7 – 2x. Now we will substitute the value of y = 7 – 2x in (2) equation and then we get : 4x – 3 * ( 7 – 2x) = -1 Or 4x – 21 + 6x = -1 Or 4x + 6x = -1 + 21 Or 10x = 20 Or x = 20 / 10 Or x = 2 Ans. Now we observe that the given pair of linear equations is solved by the Substitution Method. In this method we find that the linear equations is first converted in the form of one variable and solved, then the value of one variable is substituted in the another equation in order to get the value of another variable.
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