A high school basketball team scored 60 points in last week’s game. The team scored a total of 27 baskets; some were two-point shots and some were three-point shots. How many two-point shots did they make? How many three-point shots did they make?
x + y = 27,
2x + 3y = 60
What is the solution of the system of equations, and what does it represent?
Answers
Answer:
Let's comment the system. We can see that the first equation is . It means that x and y are two quantities that sum to 27. Since we know that the team scored a total of 27 baskets, we know that x and y are something that "compose" the number of baskets. So, they must be the number of two and three points shot.
The second equation is . We know that the team scored 60 points, and that every x is "worth" 2 and every y is "worth" 3. So, x is the number of two-points shots and y is the number of three points shots.
To solve the system we can isolate y from the first equation:
and substitute this expression in the second equation:
So, we can deduce back
Now remember that x was the number of two-points shots and y was the number of three-points shots to get to the answer.
Step-by-step explanation: