Question

# Solve the following system of equations by elimination :

4X + 3Y = 6

2X - 5Y = 16

Hint:

### Perform any arithmetic operation and then find.

## The correct answer is: x = 3 and y = - 2

### Complete step by step solution:

Let 4x+ 3y=6…(i)

and 2x - 5y = 16…(ii)

On multiplying (ii) with 2, we get 2(2x - 5y = 16)

⇒ 4x - 10y = 32…(iii)

Now, we have the coefficients of x in (i) and (iii) to be the same.

On subtracting (i) from (iii),

we get LHS to be 4x - 10y - (4x + 3y) = - 10y - 3y = - 13y

and RHS to be 32 - 6 = 26

On equating LHS and RHS, we have - 13y = 26

⇒ y = - 2

On substituting the value of y in (i), we get 4x + 3× - 2 = 6

⇒ 4x - 6 = 6

⇒ 4x = 12

⇒ x = 3

Hence we get x = 3 and y = - 2

Note: We can also solve these system of equations by making the coefficients of y

to be the same in both the equations.

Now, we have the coefficients of x in (i) and (iii) to be the same.

On subtracting (i) from (iii),

we get LHS to be 4x - 10y - (4x + 3y) = - 10y - 3y = - 13y

and RHS to be 32 - 6 = 26

On equating LHS and RHS, we have - 13y = 26

On substituting the value of y in (i), we get 4x + 3× - 2 = 6

Hence we get x = 3 and y = - 2

Note: We can also solve these system of equations by making the coefficients of y

to be the same in both the equations.