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Solve this pair of equations by the graphical method: 4x+y=9 , 3y-2y=49

It's difficult to show here the graphical method, but there are many ways on how to do this.
One way is to choose three random values of x (for example, 0, 1, and 2) and get the corresponding y value by substituting these values to both equations, and plot the points on a graphing paper.
The other is to get the x- and y-intercepts of both equation, and plot them on a graphing paper.

In any case, you just have to find the point of intersection of the equations (if they are intersecting lines). Note that if they happen to be parallel, there is no solution (because no intersecting point), and if coinciding lines, they have infinite solutions.

Hope this helps~ :)

Here is a very useful webpage that can do what you asked for
First change each equation to function form, ie
y = 9-4x and y = (3x-49)/2

enter 9-4x in 1st graph and (3x-49)/2 into second graph, hit draw
http://rechneronline.de/function-graphs/

at first you can't see the solution, so change the
"range of x" and range of y values
(I entered x's from 5.8 to 6.6
and the y's from -16 to -13 to get a pretty good look at the solution)

btw, notice entering the y's from smallest to highest is consistent with the input for x's