a basketball player scored 17 timea during one game. He scored a total of 21 pts,two for each two-pt shot and one for each free throw. How many two-pt shots did he make? How many free throws?
N2+m1=21
N+m=17
subtract second equation fromfirs
N=4
M=13
To find the number of two-point shots and free throws made by the basketball player, let's analyze the given information.
We know that the player scored a total of 17 times during the game. However, this includes both two-point shots and free throws. We also know that each two-point shot contributes two points, while each free throw contributes one point.
Let's assume the player made x two-point shots and y free throws. Based on these assumptions, we can form two equations using the given information:
1. Equation for the total number of times the player scored:
x + y = 17
2. Equation for the total points scored:
2x + y = 21
Now we have a system of two equations that we can solve to find the values of x and y.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method:
From the first equation, we have:
x = 17 - y
Substituting this value of x into the second equation, we get:
2(17 - y) + y = 21
Simplifying the equation:
34 - 2y + y = 21
34 - y = 21
-y = 21 - 34
-y = -13
Multiplying both sides by -1 to isolate y:
y = 13
Now, substitute the value of y back into the first equation to find x:
x + 13 = 17
x = 17 - 13
x = 4
Therefore, the basketball player made 4 two-point shots and 13 free throws during the game.