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/5 + y/6 = 12  …… (1)

x/3 − 3y/7 = 8  …… (2)

Step 1: Remove Fractions

Multiply equation (1) by 30 (LCM of 5 and 6):

6x + 5y = 360  …… (3)

Multiply equation (2) by 21 (LCM of 3 and 7):

7x − 9y = 168  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

6x + 5y = 360

⇒ 5y = 360 − 6x

⇒ y = ^{360 − 6x}/₅  …… (5)

Step 3: Substitute the Value of y in Equation (4)

Substitute y from equation (5) into equation (4):

7x − 9( ^{360 − 6x}/₅ ) = 168

Multiply the whole equation by 5:

35x − 3240 + 54x = 840

89x = 4080

⇒ x = ⁴⁰⁸⁰/₈₉

Step 4: Find the Value of y

Substitute x = 4080/89 in equation (5):

y = ^{360 − 6(4080/89)}/₅

y = ^{(32040 − 24480)}/₄₄₅

y = ⁷⁵⁶⁰/₄₄₅

y = ¹⁵¹²/₈₉

Final Answer

∴ The solution of the given system of equations is:

x = ⁴⁰⁸⁰/₈₉ and y = ¹⁵¹²/₈₉

Conclusion

Thus, by using the substitution method, we find that the solution of the given pair of linear equations is (4080/89, 1512/89).