This method is also used to find the optimal solution of linear programming problems. Therefore, x = 3 and y = 5 by using the graphical method of solving linear equations. The two lines intersect at the point (3,5). Now, we find the point of intersection of these lines to find the values of 'x' and 'y'. Plotting these points on the coordinate plane, we get a graph like this. Let us take some values for 'x' and find the values for 'y' in the equation y = x + 2. Let us take some values for 'x' and find the values for 'y' for the equation x + y = 8. Let us take two linear equations and solve them using the graphical method.
The (x,y) values at the point of intersection give the solution for these linear equations. Once it is done, we find the point of intersection of these two lines. When we are given a system of linear equations, we graph both the equations by finding values for 'y' for different values of 'x' in the coordinate system. Graphical Method of Solving Linear EquationsĪnother method for solving linear equations is by using the graph. Therefore, by solving linear equations, we get the value of x = 3 and y = 5. Let us substitute the value of 'y' in equation (1). Step 4: Using the value obtained in step 3, find out the value of another variable by substituting the value in any of the equations. Now, by subtracting the two equations, we can cancel out the 'x' terms in both equations. Step 3: The next step is to simplify these two equations by adding or subtracting them (whichever operation is required to cancel the x terms). Multiplying all the terms in equation (2) by 2, we get,Ģ(x) + 2(3y) = 2(18). Now in equation (2), let us multiply every term by the number 2 to make the coefficients of x the same in both the equations. Step 2: The next step is to multiply either one or both the equations by a constant value such that it will make either the 'x' terms or the 'y' terms cancel out which would help us find the value of the other variable. The given set of linear equations are already arranged in the correct way which is ax+by=c or ax+by-c=0.
Step 1: Check whether the terms are arranged in a way such that the 'x' term is followed by a 'y' term and an equal to sign and after the equal to sign the constant term should be present. Let us understand the steps of solving linear equations by elimination method.
Here we make an attempt to multiply either the 'x' variable term or the 'y' variable term with a constant value such that either the 'x' variable terms or the 'y' variable terms cancel out and gives us the value of the other variable. The elimination method is another way to solve a system of linear equations. Solving Linear Equations by Elimination Method Therefore, by substitution method, the linear equations are solved, and the value of x is 2 and y is 4. Step 3: Now substitute the value of 'y' in either equation (1) or (2). Substituting the value of 'x' in 2x + 4y = 20, we get, Now, let us substitute the value of 'x' in the second equation 2x + 4y = 20. Step 2: Substitute the value of the variable found in step 1 in the second linear equation. In this case, let us find the value of 'x' from equation (1). Step 1: Find the value of one of the variables using any one of the equations. Let us understand this with an example of solving the following system of linear equations. For solving linear equations using the substitution method, follow the steps mentioned below. In the two given equations, any equation can be taken and the value of a variable can be found and substituted in another equation. Now that we are left with an equation that has only one variable, we can solve it and find the value of that variable. In the substitution method, we rearrange the equation such that one of the values is substituted in the second equation. The substitution method is one of the methods of solving linear equations. Solving Linear Equations by Substitution Method To find the value of 'x', let us simplify and bring the 'x' terms to one side and the constant terms to another side. Let us work out a small example to understand this.Ĥx + 8 = 8x - 10.
If there are any fractional terms then find the LCM ( Least Common Multiple) and simplify them such that the variable terms are on one side and the constant terms are on the other side. The variable 'x' has only one solution, which is calculated asįor solving linear equations with one variable, simplify the equation such that all the variable terms are brought to one side and the constant value is brought to the other side. By solving linear equations in one variable, we get only one solution for the given variable. It is of the form 'ax+b = 0', where 'a' is a non zero number and 'x' is a variable. A linear equation in one variable is an equation of degree one and has only one variable term.