Pair of Linear Equations in Two Variables

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NCERT mathematics class 10 Chapter 3
JUDHAJEET GHOSH
Mind Map by JUDHAJEET GHOSH, updated more than 1 year ago
JUDHAJEET GHOSH
Created by JUDHAJEET GHOSH over 3 years ago
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Pair of Linear Equations in Two Variables
  1. Geometric [Graphical] Solution
    1. Single and Unique Solution
      1. Intersecting lines
        1. Consistent
          1. If the Pair of Linear Equations are ax+by+c= 0 and Ax+By+C=0 then a/A ≠ b/B ≠ c/C
        2. No solutions at all
          1. Parallel Lines
            1. Inconsistent
              1. If the Pair of Linear Equations are ax+by+c= 0 and Ax+By+C=0 then a/A = b/B ≠ c/C
            2. Infinitely Many Solutions
              1. Identical or Overlapping Lines
                1. Consistent
                  1. If the Pair of Linear Equations are ax+by+c= 0 and Ax+By+C=0 then a/A = b/B = c/C
              2. Algebraic Solution
                1. Substitution Method
                  1. We Substitute the Value of one Variable by Expressing it in the Term of the Other Variable to Solve the Pair of Linear equations
                  2. Elimination Method
                    1. We Eliminate one Variable First to Get a Linear Equation in one Variable and Then Solving it we Find the other Variable
                    2. Cross Multiplication Method
                      1. If the Pair of Linear Equations are ax+by+c= 0 and Ax+By+C=0 then x/(b*-B*c)= y/(c*A-C*a)= 1/(a*B-A*b)
                    3. Equations Reducible to a Pair of Linear Equations
                      1. in Pair of Equations with Variables in the Denominator we change the Fraction To Another Variable
                        1. Eg. Let the Pair of Equations be 2/x+3/y= 13 and 5/x-4/y= -2
                          1. We take (1/x) as 'p' and (1/y) as 'q'
                            1. Then the Equations are 2p+3q=13 and 5p-4q=-2
                              1. After solving for 'p' and 'q' we solve for (1/x)=p and (1/y)=q
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