Q:

Which represents the solution(s) of the system of equations, y + 4 = x2 and y-x=2? Determine the solution set bygraphing(-2, 0)(-2, 0) and (2,0)(-2, 0) and (3,5)no solutions

Accepted Solution

A:
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: [tex]y + 4 = x^{2}  , y -x = 2[/tex]Now checking for the given points:(a) (-2, 0)Here, [tex]y + 4 = 0 + 4 = 4 =   (-2)^{2}  =  x^{2} \\y- x = 0 -(-2) = 2  = RHS[/tex]Hence,  (-2, 0) is the solution of the given equations.b) Checking for (2,0), as (-2, 0) is a solution as shown aboveHere, [tex]y + 4 = 0 + 4 = 4 =   (2)^{2}  =  x^{2} \\y- x = 0 +  (-2) = -2  \neq 2(RHS)[/tex]Hence,  (2, 0) is NOT the solution of the given equations.c) Checking for (3,5), as (-2, 0) is a solution as shown aboveHere, [tex]y + 4 = 5 + 4 = 9 =   (3)^{2}  =  x^{2} \\y- x = 5 -3 = 2 -  (RHS)[/tex]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.