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/3 + y/4 = 11  …… (1)

5x/6 − y/3 = −7  …… (2)

Step 1: Remove Fractions

Multiply equation (1) by 12 (LCM of 3 and 4):

4x + 3y = 132  …… (3)

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

5x − 2y = −42  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (4):

5x − 2y = −42

⇒ −2y = −42 − 5x

⇒ 2y = 5x + 42

⇒ y = ^{5x + 42}/₂  …… (5)

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

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

4x + 3( ^{5x + 42}/₂ ) = 132

Multiply the whole equation by 2:

8x + 15x + 126 = 264

23x = 138

⇒ x = 6

Step 4: Find the Value of y

Substitute x = 6 in equation (5):

y = ^{5(6) + 42}/₂

y = ^{30 + 42}/₂

y = ⁷²/₂

y = 36

Final Answer

∴ The solution of the given system of equations is:

x = 6 and y = 36

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of linear equations is (6, 36).