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if solving for x you need to make y = 0
when you solve for x then substitute the answer in the next equation and you will then solve for y
This is a linear system which can be solved most easily using elimination. To do that, subtract the two equations. That will eliminate x and leave you with: \[\bf 2y=10 \implies y = 5\]Plug this y value back in to one of the equations and solve for x.
Adding the equations will also perform the elimination, as the coefficients of y are equal but opposite in sign. \[x + y = 6\]\[x-y = -4\]\[2x = 2\]\[x=1\]\[1+y=6\]\[y=5\]
However, my feeling is that the problem author intends solution by graphing. Rearrange the two equations to give y in terms of x, then graph. The point of intersection of the lines is the solution.
elimination is easier in my opinion
My quick trick for graphing lines like this is to substitute 0 for x and y and solve for the other. This gives you a pair of points (the x and y intercepts) and you just draw a straight line through them. For example: \[x+y=6\]substitute 0 for x, find y\[0+y=6\]\[y=6\]so first point is (0,6) \[x+0=6\][\x=6\], so second point is (6,0) Draw a line through (0,6) and (6,0). Repeat for the other line.
@melody16 it doesn't really matter what you think is easier, if the instructor wants the problem done another way!
Should be able to solve these problems proficiently with all the tools in the toolbox, not just one.
Thanks, the last part is mainly what I needed. Couldn't figure out how to find the equations for the two lines. That helped a lot!
I understand, no need to scream. In his question there was no evidence that his teacher wanted him to do it a specific way, although it said to graph, it didnt indicate that was his point
I guess I wasn't very clear on that part, but the question was very vague. I kept over thinking the lines part, thinking I needed the point slope form and such, but thanks! And yeah, I'm not a him :)
@melody16 No one is screaming. "and graph" seems like a pretty clear indication that one is to graph in this problem. All too often people helping on OpenStudy tell students they should solve a problem a specific way because it is easier. Yeah, it may (or may not) be easier, but if the problem specifies it should be done with a particular approach, that's the approach the student should use.
The indication of screaming came from the exclamation point. And I already said I understand your point, no need to argue.