Solve the system of equations: 

2x + 7y = 10 and 3x + y = 6.

Solution:

Consider the equations:

2x + 7y = 10…………….. (1)

3x + y = 6………………… (2)

There can be two ways to solve this problem.

In a first way, multiply equation (1) by 3 and equation (2) by 2, we get,

6x + 21y = 30……………..(3)

6x + 2y = 12……………….(4)

The coefficients the x in equation (3) and equation (4) are the same i.e. 6.

Finally, subtract equation (4) from equation (3). We get-

6x + 21y – 6x – 2y = 30 – 12

⇒ 19y = 18

y =  18/19

In order to get the value of x, the value of y is substituted in equation (2),

3x + 18/19 = 6

3x = 6 – 18/19

3x = 96/19

x = 96/57 = 32/19

Alternatively, multiply equation (2) with 7,

21x + 7y = 42………….(5)

And equation (1) is 2x + 7y = 10

Subtracting equation (1) from equation (5), we get

19x = 32

x = 32/19

Substituting the value of x in Eqn. (1),

2(32/19) + 7y = 10

7y = 10 – 64/19

7y = 126/19

y = 18/19