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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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in a basketball game tatiana made 23 baskets . each of the baskets was worth either-example-1
User Sanosdole
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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

Explanation:

We know that Tatiana made 23 baskets in a game.


x represents two-points baskets, and
y represents three-points baskets.

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


x+y=23, which represents the total number of baskets.


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

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


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

Then, we replace this value to find the other one


x+y=23\\x+7=23\\x=23-7\\x=16

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

User Mark Lawrence
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