Question

find the value of each symbol in the system.
( \bigstar - \text{❄️} = -2 ) equation 1
( \bigstar - \text{❄️} = 1 + \text{❄️} ) equation 2
( \bigstar = square )
( \text{❄️} = square )

Explanation:

Step1: Let the sun - shaped symbol be \( S \) and the snow - flake shaped symbol be \( F \). Then Equation 1 is \( S - F=-2 \), so \( S=F - 2 \).

Step2: Equation 2 is \( S - F=1 + F \). Substitute \( S=F - 2 \) into Equation 2: \((F - 2)-F=1 + F\). Simplify the left - hand side: \(F-2 - F=1 + F\), which gives \(-2=1 + F\).

Step3: Solve for \( F \): Subtract 1 from both sides of the equation \(-2 = 1+F\), we get \(F=-2 - 1=-3\).

Step4: Substitute \( F = - 3\) into \( S=F - 2 \), then \( S=-3-2=-5\).

Answer:

The value of the sun - shaped symbol (\( S \)) is \(-5\) and the value of the snow - flake shaped symbol (\( F \)) is \(-3\). So \( \bigstar=-5\), \( \text{❄️}=-3\) (where \( \bigstar \) represents the sun - shaped symbol and \( \text{❄️} \) represents the snow - flake shaped symbol).