Elimination Method Questions 10

In this page elimination method questions 10 we are going to see solution of tenth problem from the worksheet elimination method worksheet.

Question 10

Solve the following system of linear equations by elimination-method

2/x + 2/3y  = 1/6 , 3/x + 2/y = 0

Solution:

2/x + 2/3y  = 1/6  ---- (1)

3/x + 2/y = 0  ---- (2)

Let 1/x = a and  1/y = b

2 a + (2b/3) = 1/6

(6 a + 2 b)/3 = 1/6

6 (6 a + 2 b )  = 3

36 a + 12 b = 3

Dividing the whole equation by 3 we get

12 a + 4 b = 1   ------- (1)

3 a + 2 b = 0 ---------(2)

12 a + 4 b = 1

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 a and b in both equation. In the first equation we have + 4b and in the second equation also we have + 2b and the symbols are  same so we have to subtract them for eliminating the variable b.

Multiply the second equation by 2 => 6 a + 4 b = 0

Subtracting the second equation from the first equation

12 a + 4 b = 1

6 a + 4 b = 0

(-)     (-)   (-)

--------------

6 a  = 1

a = 1/6

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

Substitute a = 1/6 in the first equation we get

12(1/6) + 4 b = 1

2 + 4 b = 1

4 b = 1- 2

4 b = -1

b = -1/4

Solution:

x = 6

y = -4

verification:

2/x + 2/3y  = 1/6

2/6 + 2/3(-4) = 1/6

1/3 -1/6 = 1/6

1/6 = 1/6          elimination method questions 10 elimination method questions 10

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