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:
2/x + 3/y = 13 …… (1)
5/x − 4/y = −2 …… (2)
Step 1: Substitute 1/x = a and 1/y = b
Let 1/x = a and 1/y = b
Then equations (1) and (2) become:
2a + 3b = 13 …… (3)
5a − 4b = −2 …… (4)
Step 2: Express One Variable in Terms of the Other
From equation (3):
2a = 13 − 3b
⇒ a = 13 − 3b/2 …… (5)
Step 3: Substitute the Value of a in Equation (4)
Substitute a from equation (5) into equation (4):
5( 13 − 3b/2 ) − 4b = −2
Multiply the whole equation by 2:
65 − 15b − 8b = −4
65 − 23b = −4
23b = 69
⇒ b = 3
Step 4: Find the Value of a
Substitute b = 3 in equation (5):
a = 13 − 9/2
a = 4/2
a = 2
Step 5: Find the Values of x and y
Since a = 1/x,
1/x = 2 ⇒ x = 1/2
Since b = 1/y,
1/y = 3 ⇒ y = 1/3
Final Answer
∴ The solution of the given system of equations is:
x = 1/2 and y = 1/3
Conclusion
Thus, by substituting 1/x = a and 1/y = b and using the substitution method, we find that the solution of the given system of equations is (1/2, 1/3).