Elimination Method Questions 9





In this page elimination method questions 9 we are going to see solution of ninth problem from the worksheet elimination method worksheet.

Question 9

Solve the following system of linear equations by elimination-method

15/ x + 2/y = 17 , 1/x + 1/y = 36/5

Solution:

 15/ x + 2/y = 17

 1/x + 1/y = 36/5

Let 1/x = a and 1/y = b

      15 a + 2 b = 17   -------- (1)

        a+b = 36/5

      5(a+b)=36

     5 a + 5 b = 36 -------- (2)

There are two unknowns in the given equations. By solving these equations we have to find the values of a and b. For that let us consider the coefficients of x and y in both equation. In the first equation we have + 15a and in the second equation also we have + 5a and the symbols are  same so we have to subtract them for eliminating the variable a.

                  15 a + 2 b = 17

(2) x 3 => 15 a + 15 b = 108

                 (-)   (-)       (-)     

                 ----------------

                      -13 b = -91

                           b = 91/13         

                            b = 7


now we have to apply the value of b in either given equations to get the value of another variable x

Substitute b = 7 in the first equation

         15 a + 2(7) = 17

         15 a + 14 = 17

            15 a = 17 – 14

                15a = 3

                   a = 3/15  

                  a = 1/5

Solution

   x = 5

   y = 1/7

verification:

15/ x + 2/y = 17

15/5 + 2/7 = 17

 3 + [2/(1/7)] = 17

 3 + 14  = 17

 17 = 17        elimination method questions 9 elimination method questions 9

Need to try other questions:

Solve each of the following system of equations by elimination-method.

  • x + 2 y = 7 , x – 2 y = 1     Solution
  • 3 x + y = 8 , 5 x + y = 10    Solution
  • x + y/2 = 4 , x / 3 + 2 y = 5   Solution
  • 11 x - 7 y = x y , 9 x - 4 y = 6 x y   Solution
  • 3/y + 5/x = 20/x y , 2/x + 5/ y = 15/x y   Solution
  • 8 x – 3 y = 5 x y , 6 x – 5 y = -  2 x y    Solution
  • 13 x+ 11 y = 70 ,11 x + 13 y = 74     Solution
  • 65 x – 336 y = 97 , 33 x – 65 y = 1     Solution
  • 2/x + 2/3y  = 1/6,3/x + 2/y = 0    Solution


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