Three variable linear system solution

Question

During a season, a basketball team scored a total of 85 points with free throws (1-pt), 2-pt baskets, and 3-pt baskets. The team had a total of 45 scoring plays and scored twice as many 2-pt baskets as 3-pt baskets.

Let x be the number of free throws, y the number of 2-pt baskets, and z the number of 3-pt baskets.

Write your answer as an ordered triple (x,y,z)

solve for x y z

Answer 1

The equations you need are:

x + 2y + 3z = 85

x + y + z = 45

y = 2z

Substitute:

x + 4z + 3z = 85

x + 2z + z = 45

Collect terms

x + 7z = 85

x +3z = 45

Subtract

4z=40

z=10

You do the rest!