**Solving Linear Equations by Elimination Method :**

Here we are going to see some example problems of solving linear equations in two variables using elimination method.

The various steps involved in the technique are given below:

**Step 1 :**

Multiply one or both of the equations by a suitable number(s) so that either the coefficients of first variable or the coefficients of second variable in both the equations become numerically equal.

**Step 2 :**

Add both the equations or subtract one equation from the other, as obtained in step 1, so that the terms with equal numerical coefficients cancel mutually.

**Step 3 :**

Solve the resulting equation to find the value of one of the unknowns.

**Step 4 : **

Substitute this value in any of the two given equations and fi nd the value of the other unknown.

**Question 1 :**

Solve by the method of elimination

(i) 2x – y = 3; 3x + y = 7

**Solution :**

2x – y = 3 ----(1)

3x + y = 7 ------(2)

The coefficient of y in the 1st and 2nd equation are same.

(1) + (2)

2x – y = 3

3x + y = 7

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

5x = 10

x = 10/5 = 2

By applying the value of x in (1), we get

2(2) - y = 3

4 - y = 3

y = 4 - 3

y = 1

Hence the solution is (2, 1).

(ii) x – y = 5; 3x + 2y = 25

**Solution :**

**x – y = 5 -------(1)**

**3x + 2y = 25 ------(2)**

**The coefficient of y in the first equation is 1, the coefficient of y in the second equation is 2. So, we have to multiply the first equation by 2.**

** 2x - 2y = 10**

** 3x + 2y = 25**

** -----------------**

** 5x = 35**

** x = 35/5**

** x = 7**

**By applying the value of x in (1), we get**

**7 - y = 5**

**y = 7 - 5**

**y = 2**

Hence the solution is (7, 2).

(iii) (x/10) + (y/5) = 14 ; (x/8) + (y/6) = 15

**Solution :**

(x/10) + (y/5) = 14 (x + 2y)/10 = 14 x + 2y = 140 -----(1) |
(x/8) + (y/6) = 15 (3x + 4y)/24 = 15 3x + 4y = 360 -----(2) |

(1) x 3 - (2)

(1) x 3 ==> 3x + 6y = 420

3x + 4y = 360

(-) (-) (-)

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

2y = 60

y = 30

By applying the value of y in (1), w get

3x + 6(30) = 420

3x + 180 = 420

3x = 420 - 180

3x = 240

x = 240/3 = 80

Hence the solution is (80, 30).

After having gone through the stuff given above, we hope that the students would have understood, "Solving Linear Equations by Elimination Method"

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