Question

The Cougars scored a total of 84 points in their basketball game last nightagainst the Bears. The Cougars made no one-point shots, and a total of38 two-point and three-point shots. Let x represent the number of two-pointshots and y represent the number of three-point shots.a. How many two-point shots did the Cougars make? How many three-pointshots did the Cougars make? Write and solve a system of equations that canbe used to solve this problem.

Answer 1

Step 1: Write out the values

For Cougars

Total Points = 84

Number of 1 point shot = 0

Number of 3 and 2 points shots = 38

Step 2: Write out the system of equations

`x+y=38---------------------(1)`

Since there are x number of two-point shots, then the total number of points from the two-point shots is 2x

Also, there are y number of three-point shots, then the total number of points from the three-point shots is 3y

Hence, the total number of points is 2x + 3y

Therefore,

`2x+3y=84----------------(2)`

Step 3: Solve the system of equation simultaneously

x + y = 38 ------ equation 1

2x + 3y = 84 ------ equation 2

Using the elimination method to eliminate x

Multiply equation 1 by 2 to get a new equation

2x + 2y = 76 ------ equation 3

Step 4: combine equation 2 and 3 and solve simultaneously

2x + 3y = 84------- equation 2

2x + 2y = 76 ------ equation 3

Subtract equation 3 from 2