Question

use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t - shirts sold.\\(x + y = 152\\),\\(8.5x + 12y = 1656\\)\
how many hats were sold?\
\\(\square\\) hats

Explanation:

Step1: Solve the first equation for y

From \( x + y = 152 \), we get \( y = 152 - x \).

Step2: Substitute y into the second equation

Substitute \( y = 152 - x \) into \( 8.5x + 12y = 1656 \):
\( 8.5x + 12(152 - x) = 1656 \)

Step3: Simplify and solve for x

Expand the equation:
\( 8.5x + 1824 - 12x = 1656 \)
Combine like terms:
\( -3.5x + 1824 = 1656 \)
Subtract 1824 from both sides:
\( -3.5x = 1656 - 1824 \)
\( -3.5x = -168 \)
Divide both sides by -3.5:
\( x = \frac{-168}{-3.5} = 48 \)

Answer:

48