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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 3 point baskets she made

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Answer:

n 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 3 point baskets she made

Step-by-step explanation:

We know that Tatiana made 23 baskets in a game.

[tex]x[/tex] represents two-points baskets, and [tex]y[/tex] represents three-points baskets.

If she scored 53 points, we would have the following relations

[tex]x+y=23[/tex], which represents the total number of baskets.

[tex]2x+3y=53[/tex], which represents the total number of points.

To solve this system, we multiply the first equation by -2, then sum and solve for [tex]y[/tex]

[tex]\left \{ {{-2x-2y=-46} \atop {2x+3y=53}} \right.\\ y=7[/tex]

Then, we replace this value to find the other one

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

Therefore, Tatiana made 7 baskets of two points and 16 baskets of three points.