Elimination Method Questions 5





In this page elimination method questions 5 solution we are going to see solution of fifth problem from the worksheet elimination method worksheet.

Question 5

Solve the following system of linear equations by elimination-method

(3/y) + (5/x) = 20/ xy  ------- (1)

 (2/x) + (5/ y) = 15/ xy  ------- (2)

(3/y) xy + (5/x) xy  = (20/xy) xy  ------- (1)

 (2/x) xy + (5/ y) xy = (15/xy) xy  ------- (2)

We need to make the given equation in the form of a x + b y = c for that first we have to multiply the first and second equations by xy

3 x + 5 y = 20 ------- (3)

2 x + 5 y = 15 ------- (4)


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

Subtracting the second equation from first equation

3 x + 5 y = 20 

2 x + 5 y = 15

(-)     (-)   (-)

-----------------         

       x = 5

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

Substitute x = 5 in the second equation we get               

2 (5) + 5 y = 15              

10 + 5 y = 15                                

5 y = 15 - 10                             

5 y = 5

y = 5/5 

y = 1 

Solution:     

   x = 5  

   y = 1

verification:

 3 x  + 5y = 20

 3(5) + 5(1) = 20

 15 + 5 = 20

 20 = 20       elimination method questions 5  elimination method questions 5

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
  • 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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