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.
\(x\) 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.
