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In a basketball game, Tatiana made 23 baskets. Each of the baskets was worth either 2 or 3 points, and Tatiana scored a total of 53 points. Let x represent the number of two-point baskets she made and y represent the number of three-point baskets she made . Write a system of equations to represent the situation and solve the system to find out how many two point and three point baskets Tatiana made.

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X+y=23 (x and y added equal the number of baskets made)

2x+3y=53 (since each basket is worth a certain amount of points, x and y must be multiplied by their amount of baskets and added together to get the total number of points)

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Answer:

Tatiana scored 7 three points baskets, and 16 two-points baskets.

Step-by-step explanation:

Givens:

  • Tatiana made 23 baskets.
  • [tex]x[/tex] represents the two-point baskets.
  • [tex]y[/tex] represents the three-point baskets.
  • Tatiana scored 53 points.

The expression for the 23 baskets made by Tatiana would be:

[tex]x+y=23[/tex]

In words, the sum of both type of scored baskets sum 23.

The expression for the total points scored would be:

[tex]2x+3y=53[/tex]

In words, baskets of two points and three points sum 53 total points scored by Tatiana.

Now, we isolate [tex]x[/tex] in the first equation and replace it in the second equation:

[tex]x=23-y\\2(23-y)+3y=53\\46-2y+3y=53\\y=53-46\\y=7[/tex]

Replacing this value in the first equation, we have:

[tex]x+y=23\\x=23-7=16[/tex]

Therefore, Tatiana scored 7 three points baskets, and 16 two-points baskets.

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