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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineFor a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Maddie purchased 7979 shares in the software company and 2020 shares in the biotech firm, which cost a total of $3,813\$3,813. At the same time, Dave invested a total of $1,977\$1,977 in 1111 shares in the software company and 2020 shares in the biotech firm. How much did each share cost?\newlineEach share in the software company cost $____\$\_\_\_\_, and each share in the biotech firm cost $____\$\_\_\_\_.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineFor a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Maddie purchased 7979 shares in the software company and 2020 shares in the biotech firm, which cost a total of $3,813\$3,813. At the same time, Dave invested a total of $1,977\$1,977 in 1111 shares in the software company and 2020 shares in the biotech firm. How much did each share cost?\newlineEach share in the software company cost $____\$\_\_\_\_, and each share in the biotech firm cost $____\$\_\_\_\_.
  1. Define Share Costs: Let's denote the cost of one share in the software company as xx dollars and the cost of one share in the biotech firm as yy dollars.
  2. Maddie's Investment Equation: Maddie's investment can be represented by the equation 79x+20y=381379x + 20y = 3813, as she bought 7979 shares of software and 2020 shares of biotech.
  3. Dave's Investment Equation: Dave's investment can be represented by the equation 11x+20y=197711x + 20y = 1977, as he bought 1111 shares of software and 2020 shares of biotech.
  4. System of Equations: We now have a system of equations to solve:\newline79x+20y=381379x + 20y = 3813\newline11x+20y=197711x + 20y = 1977
  5. Eliminate Variable yy: To eliminate yy, we can subtract the second equation from the first:\newline(79x+20y)−(11x+20y)=3813−1977(79x + 20y) - (11x + 20y) = 3813 - 1977\newline79x−11x=3813−197779x - 11x = 3813 - 1977\newline68x=183668x = 1836
  6. Solve for x: Solving for x, we divide both sides by 6868:x=183668x = \frac{1836}{68}x=27x = 27
  7. Substitute xx into Equation: Now that we have the value of xx, we can substitute it back into one of the original equations to solve for yy. Let's use the second equation:\newline11(27)+20y=197711(27) + 20y = 1977\newline297+20y=1977297 + 20y = 1977
  8. Solve for y: Subtract 297297 from both sides to solve for y:\newline20y=1977−29720y = 1977 - 297\newline20y=168020y = 1680
  9. Solve for y: Subtract 297297 from both sides to solve for yy:\newline20y=1977−29720y = 1977 - 297\newline20y=168020y = 1680Divide both sides by 2020 to find the value of yy:\newliney=168020y = \frac{1680}{20}\newliney=84y = 84

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