Solve the System of Linear Equations Using Substitution Method

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Solve the following system of equations using substitution method:

x + y/2 = 4  …… (1)

x/3 + 2y = 5  …… (2)

Step 1: Express One Variable in Terms of the Other

From equation (1):

x + y/2 = 4

⇒ x = 4 − y/2  …… (3)

Step 2: Substitute the Value of x in Equation (2)

Substitute x from equation (3) into equation (2):

(4 − y/2)/3 + 2y = 5

Step 3: Simplify the Equation

4/3 − y/6 + 2y = 5

Combine like terms:

2y − y/6 = ^{12y − y}/₆ = ^11y/₆

So,

11y/6 + 4/3 = 5

Convert all terms into fractions with denominator 6:

11y/6 + 8/6 = 30/6

⇒ 11y/6 = 22/6

⇒ 11y = 22

⇒ y = 2

Step 4: Find the Value of x

Substitute y = 2 in equation (3):

x = 4 − 2/2

x = 4 − 1

x = 3

Final Answer

∴ The solution of the given system of equations is:

x = 3 and y = 2

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of linear equations is (3, 2).