The graph of the equations 2x + 3y = 11 and x - 2y + 12 = 0 intersects at P(x1, y1) and the graph of the equation x - 2y + 12 = 0 intersects the x-axis at Q(x2, y2). What is the value of (x1 - x2 + y1 + y2) ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 15
2x + 3y = 11 eq1
x - 2y + 12 = 0 eq2
x - 2y + 12 = 0 intersects at x-axis
y = 0, x = -12
Q(x2, y2) = (-12, 0)
from eq1 and eq2
x = (11 - 3y)/2 [from eq1]
Putting in eq2
[(11 - 3y)/2 ] - 2y + 12 = 0
11 - 3y - 4y + 24 = 0
-7y = -35
y = 5, x = -2
P(x1, y1) = (-2, 5)
(x1 - x2 + y1 + y2) = (-2 + 12 + 5 + 0) = 10 + 5 = 15