What is the point of intersection of two lines, and how would I find it?

The point of intersection is where the lines would cross if we drew them on the same graph, in your exam you may be asked to find the coordinates of this point.

To do this we would first draw a sketch of the lines to see roughly where they meet, this will help us later to check our answer is right. Next rearrange the equation of one of the lines so it's in the form x= or y=. We then replace this value for x or y for that in the other equation, and simplify this to find a value for one of the coordinates. We use this coordinate to find out the other, and check these are what we'd expect from our graph.

For example, you could be asked 'Find the coordinates of the point of intersection of the lines x+2y-7=0 and 5x-y-2=0'.

From a sketch we can see that both coordinates should be positive.

Adding 7 to both sides of the first equation to get x+2y=7 and subract 2y to find x=7-2y.

Next substitute this into our other equation, so  5x-y-2=0 become 5(7-2y)-y-2=0 which simplfys to 33-11y=0 so y=3. Using this value we have 5x-3-2=0, so x=1.

These coordinates coordinates look right from out graph, and putting these values into the first equation x+2y-7=0 gives 1+6-7=0 which checks out.

So our final answer is that the point of intersection is  (1,3).