Pair of linear equations in two variables is an important Class 10 Maths topic. The elimination method helps you remove one variable and find both values step by step.
What Is the Elimination Method?
In this method, we add or subtract two equations so that one variable cancels out. We solve the remaining equation and substitute the value back to find the second variable.
Step 1: Write the Equations Clearly
Write both equations in a standard form such as ax + by = c. Keep the x terms, y terms and constants aligned.
Step 2: Make One Pair of Coefficients Equal
If the coefficients of one variable are already equal, add or subtract the equations directly. Otherwise, multiply one or both equations by suitable numbers first.
Step 3: Add or Subtract to Eliminate a Variable
Use addition when the coefficients have opposite signs and subtraction when they have the same sign. After one variable disappears, solve the resulting one-variable equation.
Step 4: Substitute and Check the Solution
Substitute your value into either original equation. Check both original equations to confirm that the ordered pair is correct.
Worked Example 1: Eliminate a Variable Directly
Solve 2x + 3y = 13 and 2x − y = 5.
- Subtract the second equation from the first: 4y = 8.
- Therefore, y = 2.
- Substitute y = 2 into 2x − y = 5: 2x − 2 = 5, so x = 7/2.
- The solution is (x, y) = (7/2, 2).
Worked Example 2: Equalise Coefficients First
For equations such as 3x + 2y = 12 and 5x + 2y = 20, the y coefficients already match. Subtract the first equation from the second to eliminate y, then substitute x back into either equation.
Common Mistakes to Avoid
- Changing the sign of only one term while multiplying an equation.
- Adding when subtraction is required, or vice versa.
- Skipping the final check in the original equations.
- Writing the answer without clearly stating x and y.
Practice Question
Solve using elimination: 4x + 3y = 18 and 2x − 3y = 0. Eliminate y first and check your answer in both equations.
Key Takeaways
- Align the equations before operating on them.
- Make one pair of coefficients equal or opposite.
- Add or subtract to eliminate one variable.
- Substitute and verify the final answer.
FAQs
What is the elimination method in linear equations?
It is a method in which addition or subtraction removes one variable so the other can be solved.
When should I add or subtract the equations?
Add opposite-signed coefficients and subtract same-signed coefficients to make one variable zero.
How do I check the solution?
Substitute both values into each original equation. Both sides should match.
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