Answer:
Step-by-step explanation:
Let x, y, z represent the numbers of 1-, 2-, and 3-point baskets, respectively. The given relations are ...
x +2y +3z = 31 . . . . . . total points scored
y -x = 5 . . . . . . . . . . . 5 more 2-point baskets than free throws
y = 3z . . . . . . . . . . . . 3 times as many 2-point baskets as 3-point baskets
Using the second equation to write an expression for x, we have ...
x = y -5
Substituting this and the third equation into the first, we get ...
(y -5) +2y +(y) = 31
4y = 36 . . . . . . . . . . . add 5, collect terms
y = 9
x = 9 -5 = 4
z = y/3 = 9/3 = 3
The player made 4 free throws, 9 2-point baskets, and 3 3-point baskets.
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Alternate solution
The equations can be written in augmented matrix form as ...
[tex]\left[\begin{array}{ccc|c}1&2&3&31\\-1&1&0&5\\0&1&-3&0\end{array}\right][/tex]
Row-reducing this matrix using any of a number of calculators gives (x, y, z) = (4, 9, 3), as above.
