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Solve the shape equation puzzles homework homework 2 -back

Solve the shape equation puzzles homework homework 2 -back-example-1

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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.

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