Submitted by Anonymous (not verified) on
for 2 (iii) i have x=y and x=2y as solutions to x^2-3xy+2y^2=0. i know i can draw straight line graphs for both of these solutions but what does it mean that (x,y) lies on one (or both ) straight lines. does it mean the origin or any point?
Try Sketching these lines and
Submitted by The indefinite ... (not verified) on
Try Sketching these lines and substitute points from the line into your function and see what happens
Straight Lines
Submitted by cxm on
If you think back a few years to when you learnt how to plot, say, y=3x+1 you probably used a table, picking a few values of x and then finding the corresponding values of y. What you have done there is to find pairs of coordinates - such as (1,4) - that satisfy y=3x+1. The lous of all points (x,y) where y=3x+1 is the (infinite) straight line (which happens to go through the few points you have plotted).
The (or both) part of the question is referring to that fact that the lines intersect, so the point (x,y) at the point of intersection lies on both lines at once.
Hope I have not made things more confusing :-)
I am also pretty confused
Submitted by Poppy (not verified) on
I am also pretty confused about this part, do we just have to state that (x,y) lies on both lines at the intersection or is there more to it?
2iii continued
Submitted by cxm on
If you solve x^2 - 3xy + 2y^2=0 (by factorising) you end up with the equations of two straight lines. This is *all* you need to do to "Show that ... then the point with coordinates (x,y) lies on one (or both) of two straight lines". The "(or both)" refers to the fact that the lines intersect so there is one point that lies on both lines. You don't have to do anything special.
You then just draw the two lines.