Substitution Approach To Solve System Of Straight line Equations

To resolve system of straight line equations, students can use substitution method. This process is extremely effective and simple when among the equations possess a variable with coefficient “one”. This process is again utilized by grade 10 or grade 11 students to resolve system of 2 or 3 straight line equations.

During this method, the requirement of the among the variables is acquired within the equations which value is substituted for the same variable within the other equation. For instance think about the machine of straight line equations with variables “a” and “b” is supplied as below:

a 3b = 5

3a – 4b = 2

Understand that in first equation, “a 3b = 5” the coefficient of “a” is “1” that is really a great hint to begin with this equation and uncover the requirement of “a” by means of “b” as described next step

a 3b = 5

a = 5 – 3b

We moved the word “3b” right hands side within the equation to resolve it for “a” so that you can isolate the variable “a”.

Next, substitute this cost of “a” within the other equation to possess that equation in a single variable “b” only as proven below:

The 2nd equation is:

3a – 4b = 2

Substitute during this equation the requirement of “a” which is equivalent to “5 – 3b” while using the brackets as proven next step:

3 (5 – 3b) – 4b = 2

Now solve the above mentioned pointed out stated equation for “b” by opening the brackets and isolating the variable “b”. Number “3” outdoors the bracket will multiply while using terms within the brackets to get “15 – 9b” to begin the brackets.

15 – 9b – 4b = 2

– 13b = 2 – 15

– 13b = – 13

b = 1

By dividing each side by “- 13” the requirement of “b” is acquired and which is equivalent to “1”.

Now, we solved just the half in the issue yet, as cost of other variable “a” remains unknown.

To obtain the cost of “a”, substitute the requirement of “b = 1” a lot of the given equations. I’ll make use of the equation “a = 5 – 3b” to replacement for “b” and to obtain the cost of “a” as proven next step:

a = 5 – 3 (1)