Pair of linear equations in Two variables.

Pair of linear equations in Two variables.

1. Meaning: Two linear equations in the same 2 variables are called a pair of linear equations in Two variables

2. General Form: a1x + b1y +c1=0 a2x+b2y+c2=0 where a1, b1, c1, a2, b2, c2 are all real numbers & a1²+b1²≠ 0, a2²+b2²≠ 0

3. Types of solutions we can get graphically:

   • • For given 2 equations a1x+ b1y+ c1=0 and a2x+ b2y+ c2= 0 the condition for getting infinite number of solutions is that a1x/ a2x= b1x/ b2y= c1/ c2
   • E
     • For 2 given equations a1x+b1y+c1 =0 and a2x+b2y+c2 =0 the condition for getting one unique solutions is that a1/a2≠b1/b2
   • • for 2 given equations a1x +b1y +c1 =0 and a2x +b2y +c2 =0 the condition for getting no solutions is that a1x/ a2x= b1y/ b2y≠ c1/ c2

4. What do you mean by solutions? Solutions are values of x and y common to both the pair of linear equations given

5. Methods of finding solutions algebraically

   • Cross- multiplication Method
   • Substitution Method
   • Elimination Method

6. Linear equation refers to an equation Of two variables which when plotted on a graph gives a straight line

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