Solve the following system of equations by elimination method:

2x + 3y = 46

3x + 5y = 74

Given pair of linear equations is

2x + 3y = 46 …(i)

And 3x + 5y = 74 …(ii)

On multiplying Eq. (i) by 3 and Eq. (ii) by 2 to make the coefficients of x equal, we get the equation as

6x + 9y = 138 …(iii)

6x + 10y = 148 …(iv)

On subtracting Eq. (iii) from Eq. (iv), we get

6x + 10y – 6x – 9y = 148 – 138

⇒ y = 10

On putting y = 10 in Eq. (ii), we get

3x + 5y = 74

⇒ 3x + 5(10) = 74

⇒ 3x + 50 = 74

⇒ 3x = 74 – 50

⇒ 3x = 24

⇒ x = 8

Hence, x = 8 and y = 10 , which is the required solution.