"Lines and angles" is one of the many topics present in GMAT syllabus. The questions can be asked in different ways in GMAT exam but one of the question can be regarding intersection of two given lines.
We can have three different conditions regarding two given lines which are:
(i) They intersect at just one point.
(ii) Lines are coincident which means, one line lies on top of other line. It means they have infinite points of intersection in this condition. So, any point which lies on one line, is also present on other line.
(iii) Lines are parallel which means they do not intersect at all.
Now, how can we know that two given lines falls under condition (i), (ii) or (iii).
Lets suppose that we have two lines ax+by=c and px+qx=r
If, we have , it means equations fall under condition (i). Hence, they have just one point of intersection.
If, we have , it means equations fall under condition (ii). Hence, they have infinite points of intersection.
If, we have , it means equations fall under condition (iii). Hence, they do not have any point of intersection.
In case two given lines have one point of intersection, how can we find coordinates of their point of intersection. There is a simple process to do so. I will explain it through an example.
Lets suppose that first given line is (2x+y=1) (1)
And, second given line is (x+y=2) (2)
To find intersection of these two given lines, we take value of one variable from any given equation and put it in the other equation. This is also called method of substitution. In other words, we need to solve these equations to find coordinates of point of intersection.
Lets suppose we take value of y from equation number (1) and put it in equation number (2).
y=1-2x from equation number (1) and putting it in (2) we get,
Now, we have value of x and we can put value of x in any of the given equation to find value of y. Lets put value of x in equation number (1), we get
So, the point of intersection is (-1, 3)
If, you have any doubt regarding this concept then feel free to leave comment.