Answered By Jesslyn C

We first want to isolate the y variable in each equation so we can see what types of functions we are dealing with. 

 

3x-y+4 =0 ->  y=3x+4

^{x^2 - 8y - 1 =0 -> y = 1/8 x^2 - 1/8}

^{now we know we have a positive linear function and a quadratic with a minimum vertex and y intercept at -1/8.} 

^{There are a few ways to solve this:}

^{1. Graph the 2 functions to see how many intersection points there are.} 

^{A. If you graph both we can see there are 2 intersection points and therefore 2 Real solutions.} 

^{2. Since the question is asking about the number of solutions and not the actual solution we need to combine the functions and find the discriminate (d=b^2 - 4ac).}

 

^{3x+4 = 1/8 x^2 -1/8}

^{8(3x+4) = x^2 - 1}

^{24x + 32 = x^2 - 1} 

^{0 = x^2 - 24x - 33}

 

^{d= (-24)^2 - 4(1)(-33) =  708}

^{since it is a positive value we know there are 2 Real solutions.}