Melissa made 5 three-point baskets in her basketball game.
Cramer's Rule is a system of linear equation solving technique.
Let's say we're given a system of linear equations.
ax+by=c
dx+ey=f
then, the solution of the equation with the Cramer's rule is given by
[tex]x= \frac{\begin{vmatrix}c&b\\f&e\end{vmatrix}}{\begin{vmatrix}a&b\\d&e\end{vmatrix}}[/tex]
[tex]y= \frac{\begin{vmatrix}a&c\\d&f\end{vmatrix}}{\begin{vmatrix}a&b\\d&e\end{vmatrix}}[/tex]
Let Melissa make 'x' 2-point baskets and 'y' 3-point baskets.
So, as she made a total of 14 baskets we have that
x+y=14
and, as she made a total of 33 points we have that
2x+3y=33
We end up with the system of linear equations.
x+y=14
2x+3y=33
This gives us the matrix equation
[tex]\left[\begin{array}{ccc}1&1\\2&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}14\\33\end{array}\right][/tex]
Using Cramer's rule we get
[tex]x= \frac{\begin{vmatrix}14&1\\33&3\end{vmatrix}}{\begin{vmatrix}1&1\\2&3\end{vmatrix}}=\frac{14 \times 3 - 1 \times 33}{1 \times 3 - 1 \times 2} = \frac{42 - 33}{3-2}=\frac{9}{1} =9[/tex]
[tex]y= \frac{\begin{vmatrix}1&14\\2&33\end{vmatrix}}{\begin{vmatrix}1&1\\2&3\end{vmatrix}}=\frac{1 \times 33 - 14 \times 2}{1 \times 3 - 1 \times 2} =\frac{33-28}{3-2}= \frac{5}{1} =5\\[/tex]
Hence, Melissa made (y=)5 three-point baskets in her basketball game.
To learn more about Cramer's rule- https://brainly.com/question/22247684?referrer=searchResults
#SPJ2
