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Noah is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Noah made a total of 11 shots altogether and scored a total of 29 points. Write a system of equations that could be used to determine the number of two point shots noah made and the number of three point shots he made. Define the variables that you use to write the system.



Answer :

The system of equations is x + y = 11 and 2x + 3y = 29 and variables are x and y.

Let us assume the number of two point shots be x and the number of three point shots be y. Forming the equation now -

x + y = 11 : Equation 1

2x + 3y = 29 : Equation 2

Rewriting the equation 1 as per x.

x = 11 - y : Equation 3

Keep the value of x form equation 3 in equation 2

2(11 - y) + 3y = 29

Performing multiplication on Left Hand Side of the equation

22 - 2y + 3y = 29

y = 29 - 22

y = 7

Keep the value of y in equation 3.

x = 11 - 7

x = 4

So, the two point shots are 4 and three points shots are 7. The variables are x and y and system of equations are equation 1 and equation 2.

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