How to Solve Simultaneous Linear Equations and Find the Value of m | Class 10 Maths
In this question, we are given a pair of simultaneous linear equations. Our first task is to find the values of x and y. Once these values are obtained, we use them to determine the value of m in the equation y = mx + 3.
This type of question is commonly asked in Class 10 Board Exams and helps students understand the concept of solving linear equations using the elimination method.
❓ Question
Solve the following system of equations:
2x + 3y = 11
2x − 4y = −24
Hence, find the value of m for which
y = mx + 3
📘 Concept Used
- Pair of Linear Equations in Two Variables
- Elimination Method
- Substitution Method
- Equation of a Straight Line
✍️ Solution
Step 1: Write the Given Equations
Equation (1):
2x + 3y = 11
Equation (2):
2x − 4y = −24
Notice that the coefficient of x is the same in both equations. Therefore, we can eliminate x directly by subtracting the two equations.
Step 2: Eliminate x
Subtract equation (1) from equation (2):
(2x − 4y) − (2x + 3y) = −24 − 11
2x − 4y − 2x − 3y = −35
−7y = −35
Divide both sides by −7.
y = 5
Step 3: Find the Value of x
Substitute y = 5 into equation (1):
2x + 3(5) = 11
2x + 15 = 11
2x = −4
Divide both sides by 2.
x = −2
Step 4: Verify the Solution
Substitute x = −2 and y = 5 into equation (2):
2(−2) − 4(5)
= −4 − 20
= −24 ✔
Hence, the obtained values satisfy both equations.
Step 5: Find the Value of m
Given,
y = mx + 3
Substitute x = −2 and y = 5.
5 = m(−2) + 3
5 − 3 = −2m
2 = −2m
m = −1
💡 Key Learning
- If the coefficient of one variable is the same in both equations, the elimination method becomes the quickest approach.
- Always substitute the obtained values back into one of the original equations to verify the solution.
- After finding the values of x and y, use them carefully in the given relation to determine the unknown constant.
📝 Final Answer
x = −2
y = 5
m = −1
📚 Conclusion
By applying the elimination method, we obtained the solution of the pair of linear equations as x = −2 and y = 5. Substituting these values into the equation y = mx + 3 gives m = −1. This problem demonstrates how solving simultaneous equations can be used to determine unknown constants in related equations.