Elimination Method Questions 6

In this page elimination method questions 6 we are going to see solution of sixth problem from the worksheet elimination method worksheet.

Question 6

Solve the following system of linear equations by elimination-method

8 x – 3 y = 5 x y

6 x – 5 y = - 2 x y

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

8 x – 3 y = 5 x y  ------ (1)

6 x – 5 y = - 2 x y  ------ (2)

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

8/y – 3/x = 5

6/y – 5/x = -2

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

-3a + 8 b = 5 ------- (3)

- 5a + 6 b = -2 ------- (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 a and b in both equation. In the first equation we have + 8 b and in the second equation also we have + 6b and the symbols are  same so we have to subtract them for eliminating the variable b.

Multiply the first equation by 6 and second equation by 8, we get

-18 a + 48 b = 30

-40 a + 48 b = -16

Subtracting the second equation from first equation

-18 a + 48 b = 30

-40 a + 48 b = -16

(+)     (-)       (+)

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

22 a   = 46

a = 46/22

a = 23/11

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

Substitute a = 23/11 in the second equation we get

-3 (23/11) + 8 b = 5

-69/11 + 8 b = 5

8 b = 5 + 69/11

8 b = (55+69)/11

b =124/(11x8)

b = 31/22

Solution:

X = 11/23

Y = 22/31

verification:

8 x - 3 y = 5 x y

8(11/23) - 3(22/31) = 5 (11/23) x (22/31)

(88/23)-(66/31)=5(242)/713

(2728-1518)/713 =1210/713

1210/713 = 1210/713   elimination method questions 6 elimination method questions 6  elimination method questions 6

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
• 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