Equating the coefficients solve the following equations by method of elimination

2x + y = 12

5x – 3y = 16

As the name holds, method of elimination literally uses elimination technique.

We have,

2x + y = 13 …(i)

5x – 3y = 16 …(ii)

In order to eliminate one of the variables (x and y), we need to make that variable’s coefficient equal in both of the equations.

In this question, it is easy to eliminate y, since both the equations have different signs for variable y. That is, equation (i) has a (+) sign before y and equation (ii) has a (-) sign before y.

Now, we need to make the coefficient of y equal, since in equation (i), y’s coefficient is 1 and in equation (ii), y’s coefficient is 3 (ignoring the signs before it).

For equal coefficient of y, multiply equation (i) by 3. (Multiplication has to be done over the whole equation as to balance the equation even after making changes)

So, we have

2x + y = 13 [× 3

⇒ 6x + 3y = 36 …(iii)

Now, we have equations (iii) and (ii) which can be solved by eliminating variable y.

Recall equation (iii) and (ii),

6x + 3y = 39

5x – 3y = 16

Solve these,

We get,

11x = 55

⇒ x = 5

Put this values of x in equation (i), we get

2(5) + y = 13

⇒ 10 + y = 13

⇒ y = 13 – 10

⇒ y = 3

Thus, we get our solution as x = 5 and y = 3.