Question

Solve the following system of equations or show that it does not have a real solution. Support your answer analytically and graphically. y=x²-4, y=-(x+5)

Answer 1

these equations have no solution in the domain of real numbers

Explanation:

Hello! To solve this problem of equations first let's equate equations one and two and perform the procedure to find X

`Y=x^2-4\\Y=-x-5`

`x^2-4=-X-5\\x^2+X+1=0`

if we solve the quadratic equation we find the following results

`X1=-(1)/(2) +\frac{ \sqrt[2]{3} }{2}i\\X2=-(1)/(2) -\frac{ \sqrt[2]{3} }{2}i`

as we can see the two answers result in imaginary numbers which means that the two equations are not intercepted I attached a picture of the graph