Answer:
He made 5 2-pointers and 4 3-pointers
Explanation:
Let x = number of 2-pointers he scored.
Let y = number of 3 pointers he scored.
The total number of shots he made is x + y, and it it equals 9.
The first equation is
x + y = 9
The total number of points he scored on 2-pointers is 2x. The total number of points he scored on 3-pointers is 3y. The total number of points he scored with 2-pointers and 3-pointers is 2x + 3y. It equals 22.
The second equation is
2x + 3y = 22
We have a system of 2 equations.
x + y = 9
2x + 3y = 22
We will use the substitution method.
Solve the first equation for x.
x = 9 - y
Now substitute 9 - y in for x in the second equation.
2x + 3y = 22
2(9 - y) + 3y = 22
18 - 2y + 3y = 22
y + 18 = 22
y = 4
Now we substitute 4 for y in the first equation and solve for x.
x + y = 9
x + 4 = 9
x = 5
Answer: He made 5 2-pointers and 4 3-pointers
Check:
5 2-pointers and 4 3-popinters are a total of 9 shots, so the number of shots is correct.
Now we check the number of points.
5 * 2 + 4 * 3 = 10 + 12 = 22
22 points is the correct total.
Our answer is correct.