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

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) (Show Source): You can put this solution on YOUR website!
First let's graph

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

Graph of

Now let's move onto the second equation

Start with the given equation

Divide both sides by 2 to solve for y

Now let's graph

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 of

Now let's plot the two graphs together:

Graph of (red) (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

Take the 2nd equation and plug in

Multiply

Take the square root of both sides

So we then get or

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

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