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/2 + y/3 = 2 …… (1)
x/3 + y/2 = 13/6 …… (2)
Step 1: Remove Fractions
Multiply equation (1) by 6:
3x + 2y = 12 …… (3)
Multiply equation (2) by 6:
2x + 3y = 13 …… (4)
Step 2: Express One Variable in Terms of the Other
From equation (3):
3x + 2y = 12
⇒ 2y = 12 − 3x
⇒ y = 6 − 3x/2 …… (5)
Step 3: Substitute the Value of y in Equation (4)
Substitute y from equation (5) into equation (4):
2x + 3( 6 − 3x/2 ) = 13
2x + 18 − 9x/2 = 13
Multiply the whole equation by 2:
4x + 36 − 9x = 26
−5x = −10
⇒ x = 2
Step 4: Find the Value of y
Substitute x = 2 in equation (5):
y = 6 − 3(2)/2
y = 6 − 3
y = 3
Final Answer
∴ The solution of the given system of equations is:
x = 2 and y = 3
Conclusion
Thus, by using the substitution method, we find that the solution of the given pair of linear equations is (2, 3).