SOLUTION: Solve the system by graphing. x – 2y = 8 x + y = –1

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Question 113307: Solve the system by graphing.
x – 2y = 8
x + y = –1
Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-2y=8

1x%2By=-1





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x-2y=8 Start with the given equation



-2y=8-x Subtract +x from both sides



-2y=-x%2B8 Rearrange the equation



y=%28-x%2B8%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%288%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-4 Reduce



Now lets graph y=%281%2F2%29x-4 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-4%29+ Graph of y=%281%2F2%29x-4




So let's solve for y on the second equation


1x%2By=-1 Start with the given equation



1y=-1-x Subtract +x from both sides



1y=-x-1 Rearrange the equation



y=%28-x-1%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%28-1%29%2F%281%29 Break up the fraction



y=-x-1 Reduce





Now lets add the graph of y=-x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-4%2C-x-1%29+ Graph of y=%281%2F2%29x-4(red) and y=-x-1(green)


From the graph, we can see that the two lines intersect at the point (2,-3) (note: you might have to adjust the window to see the intersection)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
To graph an equation of a straight line, you only need to determine two points. Pick a value for x and then solve for y to give a point on the line. Do this twice for each line. Once you have your two points determined, plot them and connect the dots with a straight line.

I'll do the first one:

x-2y=8. I pick the value 4 for x first.
4-2y=8
-2y=4
y=-2 So now we know that one point is (4, -2). We'll call that point A

x-2y=8. I pick the value 0 for x next.
0-2y=8
y=-4 So our other point is (0, -4). We'll call that point B

I'll leave you to figure two points for the second equation, but I'll show a graph of both lines so that we can see where the simultaneous solution point occurs.



It looks like the lines intersect at (2, -3).

Let's check:
2-2%28-3%29=2%2B6=8, so the point is on one of the lines.
2%2B%28-3%29=-1, so the point is on the other line as well and the answer checks.