How to Solve Equations How to Solve Equations We say that the equation is the combination of variables and the constants placed on both sides of the equation. In order to find the values of the variables in the equation, we need to solve the equations. solving equations in mathematics is a very systematic and step by step procedure. Let us first take the linear equations with one variable. In order to solve the linear equation with one variable, we need to bring the terms with the variables on one side of the equation and constant terms to another side of the equation. Thus we get the value of the unknown variable. We must remember that while moving the terms from one side of the equation to another side, we need to change the signs as follows: +ve sign changes to negative and the –ve sign changes to +ve. In the same way multiplication is replaced to division and division is replaced by multiplication. Let us consider the following equation: 3x + 5 = -7x + 15
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To solve the above equation, we will bring the terms with the variables on one side of the equation and the constants are taken to another side of the equation and get the following: 3x + 7x = 15 – 5 Or we write 10 x = 10 Now we observe that 10 and x are multiplied on the left side of the equation, so we move 10 to another side of the equation and the operation changes into division. Thus we write: X = 10 / 10 X = 1 Ans. To get the value of the variables we can also use the method of hit and trial. In this method, we will place the different values of the variables in the given equation and check which value satisfies the equation. If the left side of the equation and the right side of the equation are equal, then we conclude that the particular value of the value is the solution of the given equation. Now in the above given equation, 3x + 5 = -7x + 15 we say that to find the solution of the equation, we first place the value of x = 0, we get: 3 * 0 + 5 = -7 * 0 + 15 Or 5 = 15, which is not true. Now we assume x= 1, and we get:
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3 * 1 + 5 = -7 * 1 +15 Or 3 + 5 = -7 + 15 Or 8 = 8 Hence we come to the conclusion that x = 1 is the solution to the given equation. Now we will check how to find the solution for the pair of linear equations with two variables. For finding the solution, in terms of x and y, we say that the values of x and y will satisfy both the equations. It can be done by graphic or by algebra method. Through graph, we can get the solution to the given pair of equation by plotting the graph and then observe the meeting point of both the lines. It means at this particular point, both the lines will have the same values and hence it is the solution.
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