Elimination Method
Add or subtract equations to cancel a variable.
About this topic
Elimination, also known as addition, solves a system by adding or subtracting the equations so that one variable cancels out. If the coefficients do not match, multiply one or both equations by suitable numbers first so that a variable has opposite coefficients.
After eliminating, you solve the single-variable equation and substitute back to find the other variable. For x + y = 10 and x − y = 4, adding gives 2x = 14, so x = 7 and y = 3. For 2x + 3y = 12 and 5x − 2y = 11, multiply the first by 2 and the second by 3 to make the y terms 6y and −6y, then add.
Elimination is the best choice when both equations are in standard form, and it is the basis of the row operations used in matrices and computer algebra systems that solve hundreds of equations at once. Chemists use it to balance equations, and circuit designers use it for currents.
Be careful to multiply every term of an equation, including the constant, and to subtract carefully when you change signs. A result like 0 = 7 means no solution, and 0 = 0 means infinitely many.
Key ideas
- Align the equations
- Multiply to match coefficients
- Add to eliminate
Quick check
Use cases: where Elimination Method helps
- Homework: review the key idea behind Elimination Method before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Elimination Method without notes.
- Visual learning: play with the interactive lab to see how Elimination Method changes when you adjust its inputs.
- Teaching a friend: explain Elimination Method in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Elimination Method?
Add or subtract equations to cancel a variable.
What will I learn in Elimination Method?
Align the equations. Multiply to match coefficients. Add to eliminate.
Is Elimination Method part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Elimination Method lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Elimination Method?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.