Let \( g \) be the number of points scored by each girl and \( b \) be the number of points scored by each boy.
From the problem, we can set up the following equations based on the information given:
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The total points scored by the girls and boys: \[ 3g + 2b = 23 \]
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The difference between the points scored by the girls and boys: \[ 3g - 2b = 7 \]
We can solve these two equations simultaneously.
Step 1: Solve for one variable
Let's first solve the second equation for \( 3g \): \[ 3g = 2b + 7 \]
Step 2: Substitute into the first equation
Now, we substitute \( 3g \) in the first equation: \[ (2b + 7) + 2b = 23 \]
Combine the terms to simplify: \[ 4b + 7 = 23 \]
Step 3: Solve for \( b \)
Subtract 7 from both sides: \[ 4b = 16 \]
Now, divide by 4: \[ b = 4 \]
Step 4: Substitute back to find \( g \)
Now that we have \( b \), we can substitute it back into the equation for \( 3g \): \[ 3g = 2(4) + 7 = 8 + 7 = 15 \]
Now, divide by 3 to find \( g \): \[ g = 5 \]
Final Answer: Each girl scored \( 5 \) points, and each boy scored \( 4 \) points.
Thus, the results are:
- Points scored by each girl: \( \boxed{5} \)
- Points scored by each boy: \( \boxed{4} \)