**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 how to solve system of linear equations using elimination method.

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