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

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

- back to worksheet
- Solve by graphing method
- Solve by substitution
- Synthetic Division
- Rational Expressions
- Rational Zeros Theorem
- LCM -Least Common Multiple
- GCF-Greatest Common Factor
- Simplifying Rational Expressions
- Factoring Polynomials
- Factoring a Quadratic Equation
- Factoring Worksheets
- Framing Quadratic Equation From Roots
- Framing Quadratic Equation Worksheet
- Remainder Theorem
- Relationship Between Coefficients and roots
- Roots of Cubic equation
- Roots of Polynomial of Degree 4
- Roots of Polynomial of Degree 5

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