SOLUTION: 10. Solve the following system both by graphing and then check result algebraically. y = 8 2y = x^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 10. Solve the following system both by graphing and then check result algebraically. y = 8 2y = x^2       Log On


   

Question 113829: 10. Solve the following system both by graphing and then check result algebraically.
y = 8
2y = x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's graph y=8

In order to graph y=8, simply draw a horizontal line through the y=8

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+8%29+ Graph of y=8


Now let's move onto the second equation 2y=x%5E2

2y=x%5E2 Start with the given equation


y=x%5E2%2F2 Divide both sides by 2 to solve for y


Now let's graph y=x%5E2%2F2


In order to do so, let's make a table by plugging in x-values (you get to choose which ones) to find the y-values 


       x          y
   -5.00000   12.50000
   -4.00000    8.00000
   -3.00000    4.50000
   -2.00000    2.00000
   -1.00000    0.50000
    0.00000    0.00000
    1.00000    0.50000
    2.00000    2.00000
    3.00000    4.50000
    4.00000    8.00000
    5.00000   12.50000



Now let's plot these points and connect them to get this graph


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2F2%29+ Graph of y=x%5E2%2F2


Now let's plot the two graphs together:

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C8%2C+x%5E2%2F2%29+ Graph of y=8 (red) y=x%5E2%2F2 (green)


From the graph, we can see that the two lines intersect at x=-4 and x=4 which means the solutions are (-4,8) or (4,8)





=====================================


Now let's solve algebraically:

Start with the given system
y=8
2y=x%5E2


2%288%29=x%5E2 Take the 2nd equation and plug in y=8


16=x%5E2 Multiply


Take the square root of both sides


So we then get x=-4 or x=4

So this means our solutions are (-4,8) or (4,8) (remember y is always 8 since the first equation is y=8)