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/7 + y/6 = 3  …… (1)

x/2 − y/3 = 5  …… (2)

Step 1: Remove Fractions

Multiply equation (1) by 42 (LCM of 7 and 6):

6x + 7y = 126  …… (3)

Multiply equation (2) by 6 (LCM of 2 and 3):

3x − 2y = 30  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (4):

3x − 2y = 30

⇒ 2y = 3x − 30

⇒ y = ^{3x − 30}/₂  …… (5)

Step 3: Substitute the Value of y in Equation (3)

Substitute y from equation (5) into equation (3):

6x + 7( ^{3x − 30}/₂ ) = 126

Multiply the whole equation by 2:

12x + 21x − 210 = 252

33x = 462

⇒ x = 14

Step 4: Find the Value of y

Substitute x = 14 in equation (5):

y = ^{3(14) − 30}/₂

y = ^{42 − 30}/₂

y = ¹²/₂

y = 6

Final Answer

∴ The solution of the given system of equations is:

x = 14 and y = 6

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of linear equations is (14, 6).