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- 1. GRAPHICAL SOLUTIONS OF A LINEAR EQUATION• Let us consider the following system of two simultaneous linear equations in two variable.• 2x – y = -1• 3x + 2y = 9 Here we assign any value to one of the two variables and then determine the value of the other variable from the given equation.
- 2. For the equation2x –y = -1 ---(1) X 0 22x +1 = y Y 1 5Y = 2x + 13x + 2y = 9 --- (2)2y = 9 – 3x 9- 3x X 3 -1Y = ------- 2 Y 0 6
- 3. Y (-1,6) (2,5) (0,1) (0,3)X’ X X= 1 Y’ Y=3
- 4. x + 2y = -1 x = -2y -1 ------- (iii) Substituting the value of x in equation (ii),we get 2x – 3y = 12 2 ( -2y – 1) – 3y = 12 - 4y – 2 – 3y = 12 - 7y = 14 , y = -2 ,
- 5. SUBSTITUTIONPutting the value of y in eq (iii), we get x = - 2y -1 x = - 2 x (-2) – 1 =4–1 =3 Hence the solution of the equation is ( 3, - 2 )
- 6. • In this method, we eliminate one of the two variables to obtain an equation in one variable which can easily be solved. Putting the value of this variable in any of the given equations, the value of the other variable can be obtained.• For example: we want to solve, 3x + 2y = 11 2x + 3y = 4
- 7. Let 3x + 2y = 11 --------- (i) 2x + 3y = 4 ---------(ii)Multiply 3 in equation (i) and 2 in equation (ii) and subtracting eq iv from iii, we get 9x + 6y = 33 ------ (iii) 4x + 6y = 8 ------- (iv) 5x = 25 => x = 5
- 8. • putting the value of y in equation (ii) we get, 2x + 3y = 4 2 x 5 + 3y = 4 10 + 3y = 4 3y = 4 – 10 3y = - 6 y=-2 Hence, x = 5 and y = -2

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