The graph of the equation 5x - 2y + 1 = 0 and 4y - 3x + 5 = 0, intersect at the points (α, β). What is the value of (2α - 3β) ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4.
5x - 2y + 1 = 0
5x + 1 = 2y →eq 1
4y - 3x + 5 = 0 →eq 2
putting the value of eq 1 in eq 2
2 × (2y) - 3x + 5 = 0
10x + 2 - 3x + 5 = 0
7x + 7 = 0
x = -1 →eq3
putting value of eq 3 in eq 1
5(-1) + 1 = 2y
-4 = 2y
y = -2
so, the intersection point P(α, β) = (-1, -2)
hence α = -1, β = -2
value of 2α - 3β = 2(-1) - 3(-2)
-2 + 6 = 4