1)) Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. )) The Dover High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Morton has requested 73 earth science textbooks and 100 physics textbooks for all of her classes, which costs the department a total of \( \$ 9,674 \). Mr. Delgado has asked for 68 earth science textbooks and 98 physics textbooks, which will cost a total of \( \$ 9,346 \). How much do the textbooks cost? )) Earth science textbooks cost \( \$ \square \) apiece.

Let \( x \) be the cost of an earth science textbook and \( y \) be the cost of a physics textbook. We can set up the following system of equations based on the information provided: 1) \( 73x + 100y = 9674 \) (equation from Ms. Morton's order) 2) \( 68x + 98y = 9346 \) (equation from Mr. Delgado's order) Now, to solve this system, we can use the elimination or substitution method. For this solution, let's use elimination. First, we can multiply the equations to align the coefficients of one of the variables. Let's eliminate \( y \) by making the coefficients equal: Multiply the first equation by 98 and the second equation by 100: 1) \( 73(98)x + 100(98)y = 9674(98) \) 2) \( 68(100)x + 98(100)y = 9346(100) \) This simplifies to: 1) \( 7154x + 9800y = 948652 \) 2) \( 6800x + 9800y = 934600 \) Subtract the second equation from the first: \( 7154x - 6800x = 948652 - 934600 \) This simplifies to: \( 354x = 2052 \) Now, divide both sides by 354: \( x \approx 5.78 \) (Cost of earth science textbooks) To find \( y \), substitute \( x \) back into one of the original equations. Using the first equation: \( 73(5.78) + 100y = 9674 \) This simplifies to: \( 421.74 + 100y = 9674 \) Now, isolate \( y \): \( 100y = 9674 - 421.74 \) \( 100y = 9252.26 \) Dividing by 100 gives: \( y \approx 92.52 \) (Cost of physics textbooks) Final Answer: Earth science textbooks cost \( \$ 5.78 \) apiece. Physics textbooks cost \( \$ 92.52 \) apiece.