Solve the problem using the elimination method.
-In a basketball game, Will scored 36 points, consisting only of three-point shots and two-point shots. He made a total of 15 shots. How many shots of each type did he make?
A)two-point shots: 8; three-point shots: 7
B)two-point shots: 6; three-point shots: 9
C)two-point shots: 10; three-point shots: 5
D)two-point shots: 9; three-point shots: 6

Question

Quizplus · Accepted Answer

Let x be the number of two-point shots made by Will, and y be the number of three-point shots made by Will.

From the problem, we know:

x + y = 15 (total number of shots)
2x + 3y = 36 (total number of points)

To solve for x and y, we can use the elimination method. We want to eliminate one variable (either x or y) from the equations above, so we'll multiply the first equation by -2 to get:

-2x - 2y = -30

Then we'll add this equation to the second one to get:

2x + 3y = 36
-2x - 2y = -30
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y = 6

Now that we know y = 6, we can substitute this value into the first equation to solve for x:

x + y = 15
x + 6 = 15
x = 9

Therefore, Will made 9 two-point shots and 6 three-point shots, which matches option D.

Solve the Problem Using the Elimination Method