Solve the System of 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, where x ≠ 0, y ≠ 0:

2/x + 3/y = 9/xy  …… (1)

4/x + 9/y = 21/xy  …… (2)

Step 1: Remove Denominators by Multiplying with xy

Multiply equation (1) by xy:

2y + 3x = 9  …… (3)

Multiply equation (2) by xy:

4y + 9x = 21  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

3x = 9 − 2y

⇒ x = ^{9 − 2y}/₃  …… (5)

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

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

4y + 9( ^{9 − 2y}/₃ ) = 21

4y + 3(9 − 2y) = 21

4y + 27 − 6y = 21

−2y = −6

⇒ y = 3

Step 4: Find the Value of x

Substitute y = 3 in equation (5):

x = ^{9 − 2(3)}/₃

x = ³/₃

x = 1

Final Answer

∴ The solution of the given system of equations is:

x = 1 and y = 3

Conclusion

Thus, by multiplying both equations with xy and using the substitution method, we find that the solution of the given system of equations is (1, 3).