Elimination Method Questions 4





In this page elimination method questions 4 solution we are going to see solution of fourth problem from the worksheet elimination method worksheet.

Question 4

Solve the following system of linear equations by elimination-method

11 x - 7 y = x y  ------ (1)

 9 x - 4 y = 6 x y   ------ (2)

First we have to divide the first and second equations by xy

(11 x/xy) - (7 y/xy) = xy/xy

11/y – 7/x = 1

Let 1/x be a and 1/y be b.

  -7 a + 11 b = 1

 (9 x/xy) - (4 y/xy) = 6 xy /xy 

 9/y – 4/x = 6

-4 a + 9 b = 6

-7 a + 11 b = 1   -------- (3)

 -4 a + 9 b = 6   --------- (4) 

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 b in both equation. In the first equation we have -7a and in the second equation also we have -4a and the symbols are  same so we have to subtract them for eliminating the variable b.For that we have to make the coefficients of b as same.  elimination method questions 4

Multiply the first equation by 4 => -28 a + 44 b = 4

Multiply the second equation by 7 => -28 a + 63 b = 42

Subtract the second equation from first equation

  -28 a + 44 b = 4

  -28 a + 63 b = 42

   (+)     (-)    (-)

 ---------------------

          -19 b = - 38                       

        b = -38/(- 19)

        b = 2


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

Substitute b = 2 in the second equation we get

     -28 a + 44 (2) = 4

     -28 a + 88 = 4

              -28 a = 4 - 88

              -28 a = -84

                   a = -84/(-28)

                 a = 3

Now we have to change the values of a and b in to x and y respectively.

Solution:

     X = 1/3

     Y = 1/2

verification:

 9 x  - 4 y = 6 x y

 9(1/3) - 4 (1/2) = 6 (1/3) (1/2)

3 - 2 = 1

1 = 1           elimination method questions 4 elimination method questions 4

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
  • 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
  • 15/ x + 2/y = 17 , 1/x + 1/y = 36/5  Solution
  • 2/x + 2/3y  = 1/6,3/x + 2/y = 0    Solution


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