SOLUTION: Here is the problem 11. x + y = 5 x-y = 1 I understand how they got the point on the graph. What I don't understand is how they got this answer. (3,2)

Algebra ->  Graphs -> SOLUTION: Here is the problem 11. x + y = 5 x-y = 1 I understand how they got the point on the graph. What I don't understand is how they got this answer. (3,2)       Log On


   

Question 121261: Here is the problem
11. x + y = 5
x-y = 1
I understand how they got the point on the graph. What I don't understand is how they got this answer. (3,2)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x+%2B+y+=+5………………………..(1)
x-y+=+1………………………..(2)

Solve this system:

x+%2B+y+=+5………………………..(1)… =>…x+=+-y+%2B+5
x-y+=+1………………………..(2)…substitute x and find y
-y+%2B+5+-y+=+1………………………..(2)
-2y+=+1+-+5…
-2y+=++-+4………divide both sides by -2

y+=++2………
=>…x+=+-y+%2B+5
x+=+-2+%2B+5
x+=+3
So, the point is (3,2) and it is intersection of these two lines

here is the graph:

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



Start with the given system of equations:


1x%2By=5

1x-y=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%2By=5 Start with the given equation



1y=5-x Subtract +x from both sides



1y=-x%2B5 Rearrange the equation



y=%28-x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-x%2B5 Reduce



Now lets graph y=-x%2B5 (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+-x%2B5%29+ Graph of y=-x%2B5




So let's solve for y on the second equation


1x-y=1 Start with the given equation



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



-y=-x%2B1 Rearrange the equation



y=%28-x%2B1%29%2F%28-1%29 Divide both sides by -1



y=%28-1%2F-1%29x%2B%281%29%2F%28-1%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+-x%2B5%2Cx-1%29+ Graph of y=-x%2B5(red) and y=x-1(green)


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