Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables

1. GENERAL FORM- a1x + b1y + c1 = 0 a2x + b2y + c2 = 0 a1,b1,c1,a2,b2,c2- real numbers

2. SOLUTION GRAPHICALLY- Each solution (x,y), corresponds to a point on the line representing the equation and vice-versa

3. GRAPHICAL REPRESENTATION

4. ALGEBRIC METHODS

   • By Elimination
     • Solve x-y=5, 2x-5y=4 Solution: x-y=5-------(1) 2x-5y=4---------(2) Multiplying (1) with 2 and (2) with 1 we get, (to eliminate x) 2x-2y=10 2x-5y=4 Now, (1)-(2)-----2x-2y-2x+5y=10-4 or, 3y=6 or, y=2 Now, putting the value of y in (1) (to find value of x), x=7 ___ANSWER-x=7, y=2
   • By Substitution
     • SOlve- 2x+y=8, 3x-2y=19 Solution: 2x+y=8-----(i) 3x-2y=19------(ii) From (i) x=(19+2y)/3----(iii) Now, substituting the value of x in (ii) we get, 2(19+2y)/3+y=8 or,(38+7y)/3=8 or, 7y=-14 or, y=-2 Now putting the value of y in (iii) we get, x={19+2(-2)}/3=15/3 or, x=5_____ANSWER= x=5,y=-2
   • By Cross-Multiplication
     • Solve 2x+3y=-1, 5x+y=17 Solution: By CROSS-MULTIPLICATION METHOD ( the process of cross multiplication is shown below)

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