SOLUTION: Graph the two equations {{{x^2+y^2=26}}} and {{{y=-x+8}}} and find the solutions

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Question 138687: Graph the two equations x%5E2%2By%5E2=26 and y=-x%2B8 and find the solutions
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=26 Start with the given equation


y=0%2B-sqrt%2826-x%5E2%29 Solve for y


y=sqrt%2826-x%5E2%29 or y=-sqrt%2826-x%5E2%29 Break up the right side



Now let's graph sqrt%2826-x%5E2%29

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%2826-x%5E2%29+%29+ Graph of y=sqrt%2826-x%5E2%29


Now let's graph -sqrt%2826-x%5E2%29

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-sqrt%2826-x%5E2%29+%29+ Graph of y=-sqrt%2826-x%5E2%29


Now graph y=-x%2B8

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B8++%29+ Graph of y=-x%2B8


Now graph the three equations together (note: the first two equations make up x%5E2%2By%5E2=26 )

Graph of y=sqrt%2826-x%5E2%29 (red). Graph of y=sqrt%2826-x%5E2%29 (green). Graph of y=-x%2B8(blue)


From the graph, we can see that there are no intersections. So there are no solutions.