i need help solving

Question

a basketball player scored 10 times during a game. she scored a total of 14 points, two for each two-points and one for each free throws. how many two-point shots did she make? how many free throws?

Answer 1

Let x = number of free throws she made and let y = number of two-pointers she made. We can write a system of equations to model this situation:

 

x + y = 10        (she scored 10 times)

x + 2y = 14        (each free throw is 1 point and each two-pointer is 2 points, for a total of 14 points)

 

 

Solve the first equation for x, then plug that into the second equation to solve for y:

 

x = 10 - y

 

x + 2y = 14

10 - y + 2y = 14

10 + y = 14

y = 4

 

 

Finally, plug y = 4 back into the first equation to solve for x:

 

x + y = 10

x + 4 = 10

x = 6

 

 

She made x = 6 free-throws and y = 4 two-pointers.