Smart Math guide · Algebra Smarts

Use Elimination for Systems

Add or subtract equations so one variable cancels.

All levelsWorked example includedSelf-check included
← Smart MathRelated calculators
The method

How to use it

  1. Align variables.
  2. Multiply an equation if necessary to create opposite coefficients.
  3. Add/subtract, solve, then back-substitute.
Worked example

See it in action

x+y=10 and x−y=4 → 2x=14 → x=7, y=3.

Check your thinking

How to verify it

Both equations hold: 7+3=10 and 7−3=4.

Keep learning

More Algebra Smarts guides

Algebra Smarts

Treat an Equation Like a Balance

Whatever operation you perform on one side of an equation must preserve equality on the other side.

Read guide →
Algebra Smarts

Use the Distributive Property Both Ways

Distribution expands products; factoring reverses the same structure.

Read guide →
Algebra Smarts

Spot a Difference of Squares

The identity a²−b²=(a−b)(a+b) turns some hard products and factorizations into easy ones.

Read guide →
Algebra Smarts

Solve Proportions with Structure

A proportion states that two ratios are equal; scaling or cross-products can solve the missing value.

Read guide →
CalculatorWiser

Calculators, math tools, reference tables, games, guides and a growing math library.

All calculators · Math Blog
Latest from the Math BlogWho invented mathematics?Euclid: life, ideas, and mathematical legacyWhy zero changed mathematicsMaya mathematics and calendars
Policies & trustPrivacy PolicyCookie PolicyAdvertising & Affiliate DisclosureTerms of UseDisclaimerEditorial PolicyAccessibilityPrivacy Choices