SOLVING LINEAR EQUATIONS USING ELIMINATION METHOD

Example 1 :

2x + 3y = 5

x - 3y = -2

Solution :

2x + 3y = 5 ----(1)

x - 3y = -2 ----(2)

(1) + (2) :

3x = 3

Divide both sides by 3.

x = 1

Substitute x = 1 in (1).

2(1) + 3y = 5

2 + 3y = 5

Subtract 2 from both sides.

3y = 3

Divide both sides by 3.

y = 1.

Therefore,

x = 1 and y = 1

Example 2 :

3x - 2y = 1

5x - 3y = 3

Solution :

3x - 2y = 1 ----(1)

5x - 3y = 3 ----(2)

In the above equation, none of the variables have the same coefficient in both the equations.

Let's eliminate the variable y. Consider the coefficients of y in the above two equations. The coefficients of y are 2 and 3 (without considering the sign).

Least common multiple of (2, 3) = 6.

Make the coefficient of y as 6 in both the equations multiplying by suitable factors.

And also, when you multiply, make sure that the y-terms have different signs in the two equations. So that, when you add the equations, y-terms can be eliminated.

3x(1):

9x - 6y = 3 ----(3)

-2x(2):

-10x + 6y = -6 ----(4)

(3) + (4) :

-x = -3

Multiply both sides by -1.

x = 3.

Substitute x = 3 in (1).

3(3) - 2y = 1

9 - 2y = 1

Subtract 9 from both sides.

-2y = -8

Divide both sides by -2.

y = 4.

Therefore,

x = 3 and y = 4

Example 3 :

1/2x + 1/3y = 2

1/3x + 1/2y = 13/6

Solution :

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

1/2x + 1/3y = 2 :

a/2 + b/3 = 2

Multiply both sides by 6.

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

6(a/2) + 6(b/2) = 12

3a + 2b = 12 ----(1)

1/3x + 1/2y = 13/6 :

a/3 + b/2 = 13/6

Multiply both sides by 6.

6(a/3 + b/2) = 6(13/6)

6(a/3) + 6(b/2) = 13

2a + 3b = 13 ----(2)

3x(1) :

9a + 6b = 36 ----(3)

-2x(2) :

-4a - 6b = -26 ----(4)

(3) + (4) :

5a = 10

Divide both sides by 5.

a = 2

Substitute a = 2 in (1).

3(2) + 2b = 12

6 + 2b = 12

Subtract 6 from both sides.

2b = 6

Divide both sides by 2.

b = 3

Solve for x and y :

Example 4 :

2/√x + 3/√y = 2

4/√x – 9/√y = -1

Solution :

Let a = 1/√x and b = 1/√y.

2/√x + 3/√y = 2 :

2a + 3b = 2 ----(1)

4/√x – 9/√y = -1 :

4a – 9b = -1 ----(2)

3x(1) :

6a + 9b = 6 ----(3)

(2) + (3) :

10a = 5

Divide both sides by 10.

a = 1/2

2(1/2) + 3b = 2

1 + 3b = 2

Subtract 1 from both sides.

3b = 1

Divide both sides by 3.

b = 1/3

Solve for x and y :

Example 5 :

4/x + 3y = 14

3/x – 4y = 23

Solution :

Let a = 1/x and b = y.

4/x + 3y = 14 :

4a + 3b = 14 ----(1)

3/x – 4y = 23 :

3a – 4b = 23 ----(2)

4x(1) :

16a + 12b = 56 ----(3)

3x(2) :

9a – 12b = 69 ----(4)

(3) + (4) :

25a = 125

Divide both sides by 25.

a = 5

Substitute a = 5 in (1).

4(5) + 3b = 14

20 + 3b = 14

Subtract 20 from both sides.

3b = -6

Divide both sides by 3.

b = -2

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.