Solve by elimination. Stephanie has started a small company making organic honey. She makes large and small containers She has found the costs of running her business to have a linear relationship which can be \( 5.5 x+7.5 y=930 \). She wants to sell a small container for \( \$ 12 \) and a larger container for \( \$ 15 \) and earn \( \$ 1920 \). That creates a linear relationship modeled by \( 12 x+15 y=1920 \). How many of each kind of organic should she sell fulfill her revenue and cost projections? (Hint \( 7.5 *-2=-15 \) ) Select the correct response

Solve the system of equations \( 5.5x+7.5y=930; 12x+15y=1920 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5.5x+7.5y=930\\12x+15y=1920\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{1860-15y}{11}\\12x+15y=1920\end{array}\right.\) - step2: Substitute the value of \(x:\) \(12\times \frac{1860-15y}{11}+15y=1920\) - step3: Simplify: \(\frac{12\left(1860-15y\right)}{11}+15y=1920\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{12\left(1860-15y\right)}{11}+15y\right)\times 11=1920\times 11\) - step5: Simplify the equation: \(22320-15y=21120\) - step6: Move the constant to the right side: \(-15y=21120-22320\) - step7: Subtract the numbers: \(-15y=-1200\) - step8: Change the signs: \(15y=1200\) - step9: Divide both sides: \(\frac{15y}{15}=\frac{1200}{15}\) - step10: Divide the numbers: \(y=80\) - step11: Substitute the value of \(y:\) \(x=\frac{1860-15\times 80}{11}\) - step12: Simplify: \(x=60\) - step13: Calculate: \(\left\{ \begin{array}{l}x=60\\y=80\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=60\\y=80\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(60,80\right)\) The solution to the system of equations is \( x = 60 \) and \( y = 80 \). This means that Stephanie should sell 60 small containers and 80 large containers to fulfill her revenue and cost projections.