Two ways to solve this: by algebra and by graph. as you asked for
graph, we need to plot both these lines on x-y coordinate system.
process to do that is pretty simple (for both the equations), we just
need to points to draw a line. first point can be known by using x = 0
and calculating corresponding y, then mark it on the graph. second point
can be chosen by using y = 0 and calculating corresponding x, then mark
it on the graph. Now that we have both the points, we just connect them
and see if and when they intersect.
This way, for equation 1,
points are (0,1) and (2,0). for eq. 2 points are (0,8) and (16, 0). As
you can see the lines are parallel, the will never intersect. So these
equations do not have any solution.
Just for your info, this can be done through algebra as follows:
the equations in the form of y = mx + c where m and c are constants
(numbers). In this form, for any line, m represents the slope of the
line and c represents the y-intercept of the line (point it intersects
on y-axis). On doing that, we get,
y = (-1/2)x + 1 and y = (-1/2)x + 8
As the slopes of both the equations are equal (-1/2), they are parallel and will never itnersect.
Nov 28th, 2014
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