Answer: (-3,-5), (1,3)
Step-by-step explanation: Use substitution and plug in one equation to the other where there is an isolated variable. As the two equations both have an isolated y value this allows you to set both equations equal to each other. Giving -x^2+4 = 2x+1, subtract one giving -x^2+3 = 2x then add x^2 to the other side so it will be 3 = x^2 + 2x. If you subtract three from both sides you will get the equation which is x^2 + 2x -3, you will then be able to factor that equation and get the factors (x-1),(x+3) which mean the x values are x = 1 and x = -3 to find the y value for both of these points plug in one value into one equations lets say the y = 2x+1
So we will get y = 2(1) +1 which = y = 2+1 which goes to give y = 3. So one solution is (1,3) and the next solution will be solved by finding y=2(-3)+1 which = y = -6+1 which gives y = -5 so the second solution is (-3,-5)
This makes sense that there is two solutions as you are solving for solutions between a quadratic and a line.