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  1. Glossary
  2. /Mathematics
  3. /Linear Equation

What is Linear Equation?

In short

A linear equation is an equation in which each variable has power 1, such as 2x+3y=122x + 3y = 122x+3y=12. Its graph is a straight line.

In simple words

An equation in one variable, such as 3x−5=103x - 5 = 103x−5=10, has one solution. An equation in two variables has infinitely many solutions, which are the points of a line. Two linear equations in two variables, solved together, are simultaneous equations. They can be solved by substitution, by elimination or by graphs. Their lines may cross at one point, be parallel (no solution), or lie on top of each other (infinitely many).

Example

x+y=5x + y = 5x+y=5 and x−y=1x - y = 1x−y=1. Adding gives 2x=62x = 62x=6, so x=3x = 3x=3 and y=2y = 2y=2. The lines cross at (3,2)(3, 2)(3,2).

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Related terms

  • Slope of a Line
  • Quadratic Equation

← All glossary terms

Learn it in

  1. Linear Equations and Their GraphsClass 9 to 10
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Practise

  1. The line 2x + 7y = 28 and the two axes enclose a triangle…Hard
  2. Find three solutions of 3x - y = 0. Why does its line pass through the origin?Medium
  3. A taxi charges a fixed 4 dollars and then 2.5 dollars for each kilometre…Medium
  4. The point (2, 3) lies on the line 5x + ky = 19. Find k.
Medium
All problems on this topic →

Quick questions

  1. Which point lies on both lines 2x + y = 6 and x + y = 4?Medium
  2. The graph of a linear equation in two variables isEasy
  3. To draw 4x + 3y = 24, a student plots (0, 8), (1.5, 6) and (6, 1). Which point is wrong?Hard

More Mathematics terms

  1. Algebraic Identity
  2. Arithmetic Progression
  3. Complex Number
  4. Derivative
  5. Function
  6. Isosceles Triangle
All Mathematics terms →

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