Video Transcript
Use the shown graph to solve
the given simultaneous equations. 𝑦 equals four 𝑥 minus two and
𝑦 equals negative 𝑥 plus three.
Firstly, we notice that the
graph we have been given is the graph of the two straight lines represented by
these equations. Considering the blue line,
first of all, we see that it has a 𝑦-intercept of three and a slope of negative
one. So, substituting these values
into the general equation of a straight line in its slope–intercept form, we can
see that the equation of the blue line is 𝑦 equals negative 𝑥 plus three. That’s the second of the two
equations we were given.
In the case of the green line,
we see that it has a 𝑦-intercept of negative two and a slope of four. So, substituting these values
into the general equation of a straight line, we find that the equation of this
line is 𝑦 equals four 𝑥 minus two. That’s the first equation that
we were given.
So, this figure represents
these two equations graphically, and we can therefore use it to solve them
simultaneously. The solution to this pair of
linear simultaneous equations will be the coordinates of the point that lies on
both lines. That is the point where the two
lines intersect. We can see from the graph that
the lines intersect at this single point here. And it’s a point with integer
coordinates. The 𝑥-coordinate is one, and
the 𝑦-coordinate is two. The solution to this pair of
simultaneous equations, then, is 𝑥 equals one and 𝑦 equals two.
We could, of course, check this
by substituting this pair of 𝑥-, 𝑦-values into each equation and confirming
that they do indeed satisfy each equation. Although we can see quite
clearly from our graph that this point does lie on both lines.
