Solving System Of Linear Equations By Substitution Method

Substitution Method To Solve System Of Linear Equations To solve system of linear equations, students can use substitution method.

This method is very effective and easy when one of the equations have a variable with coefficient "one". This method is again used by grade 10 or grade 11 students to solve system of two or three linear equations.

In this method, the value of the one of the variables is obtained in one of the equations and that value is substituted for the same variable in the other equation. For example; consider the system of linear equations with variables "a" and "b" is given as below: a + 3b = 5 3a - 4b = 2 Notice that in first equation, "a + 3b = 5" the coefficient of "a" is "1" and which is a good hint to start with this equation and find the value of "a" in the form of "b" as explained in the next step; a + 3b = 5 a = 5 - 3b We moved the term "3b" to the right hand side of the equation to solve it for "a" or to isolate the variable "a". Next, substitute this value of "a" in the other equation to have that equation in one variable "b" only as shown below: The second equation is: 3a - 4b = 2 Substitute in this equation the value of "a" which is equal to "5 - 3b" by using the brackets as shown in the next step: 3 (5 - 3b) - 4b = 2 Now solve the above equation for "b" by opening the brackets and isolating the variable "b". Number "3" outside the bracket will multiply with both the terms in the brackets to get "15 - 9b" to open the brackets.
15 - 9b - 4b = 2 - 13b = 2 - 15 - 13b = - 13 b = 1 By dividing both sides by "- 13" the value of "b" is obtained and which is equal to "1". Now, we solved only the half of the question yet, as value of other variable "a" is still unknown.

To find the value of "a", substitute the value of "b = 1" in any of the given equations.

I will use the equation "a = 5 - 3b" to substitute for "b" and to find the value of "a" as shown in the next step: a = 5 - 3 (1) I plugged the value of "b" in the brackets, which means "1 times 3" and solve it further. a = 5 - 3 a = 2 Hence the value of both the variables is obtained which is the solution to the given system of equations.

The solution to system of equations is "a = 2 and b = 1"