Question

The graphs of the linear equations 4x + 7y = 93 and x + 3y = 32 intersect at the point P(α, β). What is the value of (3α + 2β)?
1. 40
2. 50
3. 45
4. 47

Answer 1

Correct Answer - Option 4 : 47

Given:

Equation (1) = 4x + 7y = 93

Equation (2) = x + 3y = 32

Intersect point = P(α, β)

Concept used:

We will solve the linear equations. The value of x and y will be the cordinates of the intersenct point P.

Calculations:

⇒ 4x + 7y = 93         ----(1)

⇒ x + 3y = 32          ---(2)

4 × eq.(2) - eq (1)

⇒ 4(x + 3y) - (4x + 7y) = 4 × 32 - 93

⇒ 4x + 12y - 4x - 7y = 128     

⇒ 5y = 35

⇒ y = 35/5

⇒ y = 7

Substitute the value of y in the eq.2

 x + 3 × 7 = 32 

⇒ x + 21 = 32

⇒ x = 32 - 21

⇒ x = 11

⇒ α = 11, β = 7

(3α + 2β) = 3 × 11 + 2 × 7

⇒ 33 + 14 = 47

∴ The required value is 47