### Video Transcript

Plot the graphs of the
simultaneous equations 𝑦 equals two 𝑥 plus seven and 𝑦 equals two 𝑥 minus
four and then solve the system.

We’ll plot each of these graphs
by comparing their equations with the general equation of a straight line in its
slope–intercept form, 𝑦 equals 𝑚𝑥 plus 𝑏. The first line 𝑦 equals two 𝑥
plus seven has a slope of two and a 𝑦-intercept of seven. We can plot this line by first
plotting the 𝑦-intercept. And then for every one unit we
go to the right, we go two units up. In this case though, we’ll go
the other way. For every one unit we go to the
left, we go two units down. So that gives a point at
negative one, five; and then a point at negative two, three; and a point at
negative three, one. We can then join all of these
points up to give our first plotted line.

In the same way, we see that
the line 𝑦 equals two 𝑥 minus four has a slope of two and a 𝑦-intercept of
negative four. We can plot the
𝑦-intercept. And then, we go one unit to the
right and two units up, one unit right and two units up again, and again. And then, we join these points
up to give our second line. So, we’ve plotted the graphs of
these two simultaneous equations. But now, we’re asked to solve
the system, which means we’re looking for the point of intersection of these two
lines.

Now, our two lines don’t
intersect on the graph I’ve drawn. Does this mean that I’ve just
chosen the wrong ranges for the 𝑥- and 𝑦-axes and they would intersect if I’d
chosen a larger range? Well, the answer to that is no,
these two lines will actually never intersect. And the reason for this is
because they are parallel lines. They both have the same slope
of two. We know that parallel lines
will never meet. And therefore, these two lines
will have no point of intersection. So, in fact, there are no
solutions to this system of simultaneous equations. And our reasoning for this is
that the two equations represent parallel lines.