The Wildcats basketball team scored 18 points in the first half of the game. All the points came from either 2 or 3 point baskets. If a total of 8 shots were made ( some two pointers and some three points), how many of each type of shot were made?
X=3
If there were x 2-pointers and y 3-pointers, then we have
x+y=8
2x+3y=18
To solve this problem, we can use a system of equations. Let's assign variables to represent the number of two-point shots and three-point shots made.
Let's say x represents the number of two-point shots and y represents the number of three-point shots.
From the information given, we know that the Wildcats scored 18 points in the first half, and all of the points came from either two-point or three-point baskets. So, we can write the equation:
2x + 3y = 18
We also know that a total of 8 shots were made, so the equation for the total number of shots is:
x + y = 8
Now, we have a system of equations:
2x + 3y = 18 (Equation 1)
x + y = 8 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's solve it using the elimination method.
Multiply Equation 2 by 2 to make the coefficients of x match:
2(x + y) = 2(8)
2x + 2y = 16
Now, we can subtract Equation 1 from Equation 3 to eliminate x:
(2x + 2y) - (2x + 3y) = 16 - 18
2x + 2y - 2x - 3y = -2
-y = -2
Divide both sides of the equation by -1 to solve for y:
y = -2 / -1
y = 2
Now that we know y is 2, we can substitute this value back into Equation 2 to solve for x:
x + 2 = 8
x = 8 - 2
x = 6
Therefore, there were 6 two-point shots and 2 three-point shots made by the Wildcats basketball team in the first half of the game.