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1475050 634780970474440000

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This document discusses two methods for graphically solving systems of linear equations: 1) Assign a value to one variable and determine the value of the other variable from the equations. Plot the points and find the intersection point, which is the solution. 2) Eliminate one variable to obtain an equation in one variable, solve for this variable, then substitute back into an original equation to find the value of the other variable. The solution is the pair of values for the two variables. The document provides an example using each method to solve the system 3x + 2y = 11 and 2x + 3y = 4.

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1475050 634780970474440000
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.
For the equation 2x –y = -1 ---(1) 2x +1 = y Y = 2x + 1 3x + 2y = 9 --- (2) 2y = 9 – 3x 9- 3x Y = ------- 2 X 0 2 Y 1 5 X 3 -1 Y 0 6
X’ Y’ (2,5) (-1,6) (0,3)(0,1) X= 1 Y=3 Y X (2,5) (0,3) (2,5) (0,3) (2,5) (0,3) (2,5) (0,3) (2,5) (0,3) (2,5) (0,3) (2,5) (-1,6) (0,3) (2,5) (0,1) (-1,6) (0,3) (2,5) (0,1) (-1,6) (0,3) (2,5)
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 ,
SUBSTITUTION Putting 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 )
• 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
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
• 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
1475050 634780970474440000

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1475050 634780970474440000

  • 2. 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.
  • 3. For the equation 2x –y = -1 ---(1) 2x +1 = y Y = 2x + 1 3x + 2y = 9 --- (2) 2y = 9 – 3x 9- 3x Y = ------- 2 X 0 2 Y 1 5 X 3 -1 Y 0 6
  • 5. 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 ,
  • 6. SUBSTITUTION Putting 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 )
  • 7. • 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
  • 8. 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
  • 9. • 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