Question

9 systems of equations: word problem practice objective: use the desmos graphing calculator to solve these real - world scenarios. for the first five, the equations are provided. for the last five, you must write the equations before graphing. the basketball game in a basketball game, a player scored 26 points consisting only of 2 - point shots and 3 - point shots. if the player made a total of 11 shots, how many were 2 - pointers (x) and how many were 3 - pointers (y)?

Explanation:

Step1: Define variables and set up equations

Let \( x \) be the number of 2 - point shots and \( y \) be the number of 3 - point shots. We know two things: the total number of shots is 11, so \( x + y=11\); and the total number of points is 26, since each 2 - point shot is 2 points and each 3 - point shot is 3 points, we have \( 2x + 3y = 26\).
From the first equation \( x + y=11\), we can express \( x\) in terms of \( y\) as \( x=11 - y\).

Step2: Substitute and solve for y

Substitute \( x = 11-y\) into the second equation \( 2x+3y = 26\).
\[

$$\begin{align*} 2(11 - y)+3y&=26\\ 22-2y + 3y&=26\\ 22 + y&=26\\ y&=26 - 22\\ y&=4 \end{align*}$$

\]

Step3: Solve for x

Now that we know \( y = 4\), substitute \( y = 4\) into \( x=11 - y\).
\( x=11 - 4=7\)

Answer:

The number of 2 - pointers (\( x\)) is 7 and the number of 3 - pointers (\( y\)) is 4.