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 + 2y = 3/2 …… (1)
2x + y = 3/2 …… (2)
Step 1: Express One Variable in Terms of the Other
From equation (1):
x = 3/2 − 2y …… (3)
Step 2: Substitute the Value of x in Equation (2)
Substitute x from equation (3) into equation (2):
2( 3/2 − 2y ) + y = 3/2
Step 3: Simplify the Equation
3 − 4y + y = 3/2
3 − 3y = 3/2
Multiply both sides by 2:
6 − 6y = 3
⇒ −6y = −3
⇒ y = 1/2
Step 4: Find the Value of x
Substitute y = 1/2 in equation (3):
x = 3/2 − 2( 1/2 )
x = 3/2 − 1
x = 1/2
Final Answer
∴ The solution of the given system of equations is:
x = 1/2 and y = 1/2
Conclusion
Thus, by using the substitution method, we find that the solution of the given pair of linear equations is ( 1/2 , 1/2 ).