Answer:
The points (-2, 0) and (3,5) are the ONLY solutions of the given sets of equations.
Step-by-step explanation:
Here, the given equations are: ![y + 4 = x^{2} , y -x = 2](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%20x%5E%7B2%7D%20%20%2C%20y%20-x%20%3D%202)
Now checking for the given points:
(a) (-2, 0)
Here, ![y + 4 = 0 + 4 = 4 = (-2)^{2} = x^{2} \\y- x = 0 -(-2) = 2 = RHS](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%200%20%2B%204%20%3D%204%20%3D%20%20%20%28-2%29%5E%7B2%7D%20%20%3D%20%20x%5E%7B2%7D%20%5C%5Cy-%20x%20%3D%200%20-%28-2%29%20%3D%202%20%20%3D%20RHS)
Hence, (-2, 0) is the solution of the given equations.
b) Checking for (2,0), as (-2, 0) is a solution as shown above
Here, ![y + 4 = 0 + 4 = 4 = (2)^{2} = x^{2} \\y- x = 0 + (-2) = -2 \neq 2(RHS)](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%200%20%2B%204%20%3D%204%20%3D%20%20%20%282%29%5E%7B2%7D%20%20%3D%20%20x%5E%7B2%7D%20%5C%5Cy-%20x%20%3D%200%20%2B%20%20%28-2%29%20%3D%20-2%20%20%5Cneq%202%28RHS%29)
Hence, (2, 0) is NOT the solution of the given equations.
c) Checking for (3,5), as (-2, 0) is a solution as shown above
Here, ![y + 4 = 5 + 4 = 9 = (3)^{2} = x^{2} \\y- x = 5 -3 = 2 - (RHS)](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%205%20%2B%204%20%3D%209%20%3D%20%20%20%283%29%5E%7B2%7D%20%20%3D%20%20x%5E%7B2%7D%20%5C%5Cy-%20x%20%3D%205%20-3%20%3D%202%20-%20%20%28RHS%29)
Hence, (3,5), is the solution of the given equations.
Hence, the points (-2, 0) and (3,5) are the ONLY solutions of the given sets of equations.