Question

Solve using elimination method:
2x + 3y = 11
2x – 4y = –24

The 10-Second Trick

When the coefficient of x (or y) is the same in both equations, just subtract! No need to multiply — eliminate in one line.

Step-by-Step Solution

Step 1: Identify matching coefficients

Both equations have 2x. That means we can eliminate x directly by subtracting (ii) from (i).

2x + 3y = 11 …(i)

2x – 4y = –24 …(ii)

Step 2: Subtract

(2x – 2x) + (3y – (–4y)) = 11 – (–24)

7y = 35

y = 5

Step 3: Back-substitute

Put y = 5 in equation (i):

2x + 3(5) = 11

2x + 15 = 11

2x = –4

x = –2

✓ Answer

x = –2, y = 5

Verification

Substitute into equation (ii):

2(–2) – 4(5) = –4 – 20 = –24 ✅

Video Solution

Practice Questions

  1. 5 apples + 3 mangoes = ₹65, 2 apples + 3 mangoes = ₹35. Find cost of each fruit. (Answer: Apple = ₹10, Mango = ₹5)
  2. Solve: 3x + 2y = 12, 3x – y = 3 (Answer: x = 2, y = 3)

Also Appears In

  • CBSE Class 10 Board Exams (3-5 marks)
  • SSC CGL Tier 1 (Algebra section)
  • RRB NTPC (Mathematics section)