Basketball 83137

In the basketball game, the players threw 37 times, including 2-pointers and 3-pointers, for a total of 82 points. How many were 2 points, and how many were 3 points?

Correct answer:

a =  29
b =  8

Step-by-step explanation:

$$\begin{gathered} a+b=37 \\ 2a+3b=82 \\ a+b=37 \\ 2\cdot a+3\cdot b=82 \\ a+b=37 \\ 2a+3b=82 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a+3b=82 \\ a+b=37 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a+3b=82 \\ -0.5b=-4 \\ b=\frac{-4}{-0.5}=8 \\ a=\frac{82-3b}{2}=\frac{82-3\cdot 8}{2}=29 \\ a=29 \\ b=8 \end{gathered}$$

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