C
CraftExam
medium difficulty6 min

Algebraic solution by elimination

The elimination method solves a pair by making one variable cancel when the equations are added or subtracted.

In one line: Match, cancel, solve, and return.

Practice This Concept

Understand it

This method is useful when the coefficients of one variable are already equal or can be made equal by multiplying one or both equations. After elimination, only one variable remains, and we solve it first. Then we substitute back to get the second variable.

Example

For 2x + 3y = 13 and 2x - y = 5, subtracting the second from the first removes x immediately.

Formula and rule

Make the coefficients of one variable equal if needed, then add or subtract the equations to eliminate that variable.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1For 3x + 2y = 16 and 3x - 4y = 4, subtract the second from the first: 6y = 12, so y = 2.
  2. 2Substitute into 3x + 2y = 16 to get 3x + 4 = 16, so x = 4.

Method you can reuse

  1. 1Look for a variable with equal or opposite coefficients.
  2. 2If needed, multiply one or both equations to match coefficients.
  3. 3Add or subtract to eliminate one variable.
  4. 4Solve the remaining equation.
  5. 5Substitute back to find the second variable.

Visual tip

A small alignment table of coefficients can help decide whether addition or subtraction should be used.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the main goal of elimination in a pair of linear equations?

Think first, then show answer
The main goal is to cancel one variable so that only one variable remains. Then the simpler single-variable equation can be solved easily.

Common wrong answer

A common wrong answer is to multiply one equation correctly but then forget to multiply every term, including the constant term.

Don't mix this up

Students often add when subtraction is needed, or subtract when addition is needed, so the intended variable does not cancel.

Exam tip

Before operating on the equations, check which variable will cancel faster and choose the sign carefully.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

The exam may ask for the elimination method directly or for the first equation to be multiplied before elimination.
  1. 1

    Enough for 1 mark

    The elimination method solves a pair by making one variable cancel when the equations are added or subtracted.

  2. 2

    Add for 2 marks

    Example: For 2x + 3y = 13 and 2x - y = 5, subtracting the second from the first removes x immediately.

  3. 3

    Add for 3 marks

    This method is useful when the coefficients of one variable are already equal or can be made equal by multiplying one or both equations.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept