SOLUTION: My daughter is frustrated in Algebra II (well all math in general that is). She was given homework in which I cannot assist her with; It's been about 25-years for me. I was good at

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Question 490180: My daughter is frustrated in Algebra II (well all math in general that is). She was given homework in which I cannot assist her with; It's been about 25-years for me. I was good at it, but need a refresher in order to assist her. Here is a simple graphing problem:
y = x - 2
y = -2x + 7
Her book seems to miss some of the steps and I don't remember what to do. According to the answers at the back of the book her graph was in error on one of the positive lines (on the x axis she began at -7). What is the correct way to solve this simple problem?
Found 2 solutions by Earlsdon, josmiceli:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
This is a "system of equations" or "simultaneous equations (at least, where I went to school)"
y = x-2 and
y = -2x+7
Now since y = y, you can just set the two equations equal to each other thus:
x-2 = -2x+7 and solve for x. Add 2x to both sides.
3x-2 = 7 Now add 2 to both sides.
3x = 9 Finally, divide both sides by 3.
x = 3 Now you must replace the x in either of the two given equations and solve for y.
y = -2x+7 Substitute x = 3.
y = -2(3)+7 Evaluate.
y = -6+7
y = 1
The solution is (3, 1)
Another way is to graph the two given equations and find the point of intersection (if any) of the two lines.
y+=+highlight%28x-2%29
y+=+highlight_green%28-2x%2B7%29
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx-2%2C-2x%2B7%29
The lines intersect at (3, 1)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
All equations that look like these, that have the general form
+y+=+mx+%2B+b+, are straight lines.
Graphing amounts to finding a few of the points (x,y) that
lie on the given straight line.
The easiest way is to set +y+=+0+ and find +x+
Then set +x+=+0+ and find +y+
+y+=+x+-+2+
+0+=+x+-+2+
+x+=+2+
So, the point (2,0) is on the line
and
+y+=+0+-+2+
+y+=+-2+
So, the point (0,-2) is on the line
Do the same thing with the other line