Let's solve the given equations to find the values of Square and Star.
Equation 1: Square + Star = 8
Equation 2: Square x Star = 15
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.
From Equation 1, we can express Square in terms of Star:
Square = 8 - Star
Substituting this value of Square in Equation 2:
(8 - Star) x Star = 15
Expanding the equation:
8Star - Star^2 = 15
Rearranging the equation:
Star^2 - 8Star + 15 = 0
Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.
Factoring the equation:
(Star - 5)(Star - 3) = 0
Setting each factor to zero:
Star - 5 = 0 or Star - 3 = 0
Solving for Star:
Star = 5 or Star = 3
Now we have two possible values for Star. Let's substitute these values back into Equation 1 to find the corresponding values of Square.
For Star = 5:
Square = 8 - Star = 8 - 5 = 3
For Star = 3:
Square = 8 - Star = 8 - 3 = 5
Therefore, the solutions to the given equations are:
Square = 3 and Star = 5, or
Square = 5 and Star = 3.