SOLUTION: Solve the system of equations by graphing. Make sure that you label both equations and identify the solution. Check your solution. Y=x-7 X+y=11

Algebra ->  Linear-equations -> SOLUTION: Solve the system of equations by graphing. Make sure that you label both equations and identify the solution. Check your solution. Y=x-7 X+y=11      Log On


   

Question 934026: Solve the system of equations by graphing. Make sure that you label both equations and identify the solution. Check your solution.
Y=x-7
X+y=11
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=x-7
x%2By=11
______________
-x%2By=-7
x%2By=11
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-x%2By=-7

1x%2By=11





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


-x%2By=-7 Start with the given equation



1y=-7%2Bx Add +x to both sides



1y=%2Bx-7 Rearrange the equation



y=%28%2Bx-7%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%28-7%29%2F%281%29 Break up the fraction



y=x-7 Reduce



Now lets graph y=x-7 (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-7%29+ Graph of y=x-7




So let's solve for y on the second equation


1x%2By=11 Start with the given equation



1y=11-x Subtract +x from both sides



1y=-x%2B11 Rearrange the equation



y=%28-x%2B11%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%2811%29%2F%281%29 Break up the fraction



y=-x%2B11 Reduce





Now lets add the graph of y=-x%2B11 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-7%2C-x%2B11%29+ Graph of y=x-7(red) and y=-x%2B11(green)


From the graph, we can see that the two lines intersect at the point (9,2) (note: you might have to adjust the window to see the intersection)