A basketball player scored 35 times during one game he scored a total of 56 points 2
for each field goal and one for each free-throw how many field goals did he make how many free throws let x equals the number of field goals let y equal the number of free throws
Field goal: +2 points
Free throw: +1 point
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Total score: 56 points
Total attempts: 35 times
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2g+1t = 56
g + t = 35
Use elimination or substitution to solve.
Oops. Let's revise the equations, I didn't notice the last sentence.
2x + 1y = 56
x + y = 35
Let's set up a system of equations to solve this problem.
We know that the basketball player scored 35 times during the game, so the total number of field goals and free throws made must add up to 35.
1. x + y = 35 (equation 1)
We also know that the player scored a total of 56 points. Each field goal is worth 2 points, and each free throw is worth 1 point.
2. 2x + y = 56 (equation 2)
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination.
Let's solve it using elimination:
Multiply equation 1 by 2 to make the coefficient of the y term match equation 2:
2(x + y) = 2(35)
2x + 2y = 70 (equation 3)
Now we can subtract equation 2 from equation 3:
(2x + 2y) - (2x + y) = 70 - 56
2x - 2x + 2y - y = 14
y = 14
Substitute the value of y into equation 1 to find the value of x:
x + 14 = 35
x = 35 - 14
x = 21
Therefore, the basketball player made 21 field goals and 14 free throws.
To find the number of field goals (x) and free throws (y) made by the basketball player, let's create a system of equations based on the given information.
1. The basketball player scored 35 times, which means the total number of shots made is 35.
x + y = 35 (Equation 1)
2. Each field goal is worth 2 points, and each free throw is worth 1 point. The player scored a total of 56 points.
2x + y = 56 (Equation 2)
Now we have a system of equations:
x + y = 35 (Equation 1)
2x + y = 56 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use the elimination method.
Multiply Equation 1 by 2 to eliminate y terms:
2(x + y) = 2(35)
2x + 2y = 70 (Equation 3)
Now subtract Equation 2 from Equation 3:
(2x + 2y) - (2x + y) = 70 - 56
2x + 2y - 2x - y = 14
y = 14 (Equation 4)
Now substitute the value of y (14) into Equation 1:
x + 14 = 35
x = 35 - 14
x = 21 (Equation 5)
Therefore, the basketball player made 21 field goals (x) and 14 free throws (y).