Sophie is a high school basketball player. in a particular game she made some free throws (worth one point each) and some two point shots. sophie made a total of 10 shots altogether and scored a total of 18 points. determine the number of free throws sophie made and the number of two point shots she made.

Step-by-step explanation:

Let x = number of free throws Susie made.

Let y = number of 2-point shots Susie made.

Let's make a system to represent this:

x + y = 10

x + 2y = 18 (every y shot makes 2 points, x shot makes 1 point)

By subtracting one equation from the other, we can cancel out the x. This is called "elimination".

x + y = 10

-x + 2y = 18

-y = -8

y = 8

Now, since these equations should be equal, you can plug 8 in for y in any of these equations to get x.

x + 8 = 10

x + 8 = 10

- 8 -8

x = 2

Set of solutions: x = 2; y = 8.

Remember from above, x represents the amount of free throws and y represents the amount of 2-point shots.

Sophie made 2 free throws and 8 two-point shots.

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step-by-step explanation:

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