SOLUTION: This one really has me stumped. Find the exact solution(s)of the system: x^2/4-y^2=1 and x=y^2+1 a. (4,√3),(4,-√3),(-4,√3),(-4,-√3) b. (4,√3),

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Question 99123: This one really has me stumped.
Find the exact solution(s)of the system: x^2/4-y^2=1 and x=y^2+1
a. (4,√3),(4,-√3),(-4,√3),(-4,-√3)
b. (4,√3),(-4,√3)
c. (2,1),(2,-1),(4,√3),(4,-√3)
d. (4,√3),(4,-√3)
Thank you.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the second equation


Subtract 1 from both sides


Now move onto the second equation


Replace with

Add to both sides


Combine like terms


Multiply both sides by 4


Subtract 4x from both sides



Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:

or


or Now solve for x in each case


Now let's use these two x-values to find the y-values


Let's find y when x=0
Start with the second equation


Plug in x=0


Subtract 1 from both sides


Take the square root of both sides. Since you cannot take the square root of a negative number, x=0 is not in the solution



---------------------------------------------------------------------------

Let's find y when x=4
Start with the second equation


Plug in x=4


Subtract 1 from both sides


Take the square root of both sides. So when x=4, which means or


So our solution is



(4,), (4,)


which means the answer is D
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