Question

Been stuck on this for a while, I know its really simple but I can't seem to hack it.

Solve for x and y, then graph

x + y = 6
x - y =-4

Answer 1

if solving for x you need to make y = 0

Answer 2

when you solve for x then substitute the answer in the next equation and you will then solve for y

Answer 3

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.

Answer 4

Adding the equations will also perform the elimination, as the coefficients of y are equal but opposite in sign.

\[x + y = 6\]\[x-y = -4\]\[2x = 2\]\[x=1\]\[1+y=6\]\[y=5\]

Answer 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.

Answer 6

elimination is easier in my opinion

Answer 7

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.

Answer 8

@melody16 it doesn't really matter what you think is easier, if the instructor wants the problem done another way!

Answer 9

Should be able to solve these problems proficiently with all the tools in the toolbox, not just one.

Answer 10

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!

Answer 11

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

Answer 12

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 :)

Answer 13

@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.

Answer 14

The indication of screaming came from the exclamation point. And I already said I understand your point, no need to argue.