y = (x-5) (x+6)
y = x+6
-- Clear the parentheses in the first one (multiply it out):
y = x² + x - 30
-- Look at the two equations at the same time.
y = x² + x - 30
y = x + 6
Two quantities that are both equal to the same thing (y)
must be equal to each other, so you can write
x² + x - 30 = x + 6
and THAT should be easy to solve.
-- Subtract' x ' from each side:
x² - 30 = 6
-- Add 30 to each side:
x² = 36
-- Square root each side:
x = 6
and
x = -6 .
Those are the x-coordinates of the two solutions to the
original system of equations. We don't even care about
their y-coordinates, or where exactly they are on the graph.
All we need is the x-coordinate of a the mid-point of a line
segment between them.
Do you remember how to find the mid-point of a line segment ?
-- Its x-coordinate is the average of the x-coordinates of the end points.
-- Its y-coordinate is the average of the y-coordinates of the end points.
AND ...
The average of +6 and -6 is zero !
So ... the midpoint of the two solutions is on the y-axis.
Its x-coordinate is zero.
(Choice B)
