Question

Which represents the solution(s) of the system of equations, y + 4 = x2 and y-x=2? Determine the solution set by

Answer 1

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: $y + 4 = x^{2} , y -x = 2$

Now checking for the given points:

(a) (-2, 0)

Here, $y + 4 = 0 + 4 = 4 = (-2)^{2} = x^{2} \\y- x = 0 -(-2) = 2 = RHS$

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, $y + 4 = 0 + 4 = 4 = (2)^{2} = x^{2} \\y- x = 0 + (-2) = -2 \neq 2(RHS)$

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, $y + 4 = 5 + 4 = 9 = (3)^{2} = x^{2} \\y- x = 5 -3 = 2 - (RHS)$

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.