The sum of the first number & the square of a second number is 18. The difference between the square of the second number and twice the first number is 12.

Write a system of equations to represent this situation.
y=-x^2+18
y=.5x^-6

Solve the system to determine the numbers:
2 & 4

The roots are 4 & -4 but 2 & 4 are the correct answer as to what the 2 numbers were, correct?

Thank you! :)

y+x^2 = 18

x^2-2y = 12

eliminate x^2 and you have
18-y = 2y+12
3y = 6
y = 2
so, x^2 = 16, making (-4,2) and (4,2) possibilities.
If they meant positive numbers, then only (4,2) is the answer.

To represent the given situation as a system of equations, we can assign variables to the two numbers. Let's call the first number x and the second number y.

From the information given, we can write the following equations:

1. "The sum of the first number and the square of the second number is 18":
x + y^2 = 18

2. "The difference between the square of the second number and twice the first number is 12":
y^2 - 2x = 12

These two equations represent the given situation.

To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method:

From equation 1, we can isolate x:
x = 18 - y^2

Now substitute this expression for x in equation 2:
y^2 - 2(18 - y^2) = 12

Simplify the equation:
y^2 - 36 + 2y^2 = 12
3y^2 = 48
y^2 = 16
y = ±4

Now substitute the value of y into one of the original equations to find the corresponding value of x. Let's use equation 1:
x + (±4)^2 = 18

Simplify and solve for x:
x + 16 = 18
x = 18 - 16
x = 2

Therefore, the two numbers are x = 2 and y = 4.

In your statement, you mentioned that the roots of the equations are 4 and -4, but the correct solution is indeed x = 2 and y = 4. The negative value of y (-4) does not fulfill the conditions of the given problem statement. The numbers 2 and 4 satisfy both equations, as verified by substituting them back into the original system.