Question

 The graphs of the equations x + y = 8 and 2x – y = 7 intersect at the point P(α, β). Find the value of (5α + β)?

1. 25
2. 28
3. 30
4. 32

Answer 1

Correct Answer - Option 2 : 28

Given:

The two equations are x + y = 8 and 2x – y = 7.

Concept used:

Point of intersection is a point where two or more equations respective variables have same value.

Calculation:

x + y = 8 ----(1)

2x – y = 7 ----(2)

Add (1) and (2), we get

3x = 15

⇒ x = 5 ----(3)

Put value of (3) into (1), we get

5 + y = 8

⇒ y = 3

So, intersection point P(α, β) = (5, 3)

So, (5α + β)

⇒ (5 × 5) + 3

⇒ 28

∴ The value of (5α + β) is 28.