Linear systems with 2 unknowns You and a friend each purchase different quantities of the same items from a shop. In each of the cases (a)-(c) below: (i) Write down a linear system of equations that describes the purchases (ii) Write your system of equations as a matrix-vector equation (iii) Is there a unique solution to (ii)? If so, find it and write down the cost of each item. If there is no unique solution, explain whether this is because the cashier made a mistake, or because you don’t have enough information. (a) You buy 3 apples and 2 bananas for $4. Your friend buys 1 apples and 2 bananas for $2. (b) You buy 2 carrots and 6 dates for $7. Your friend buys 3 dates and 1 carrot for $3.50. (c) You buy 1 eggplant and 2 fennel for $2.50. Your friend buys 4 eggplants and 8 fennel for $8.
Linear systems with 2 unknowns You and a friend each purchase different quantities of the same items from a shop. In each of the cases (a)-(c) below: (i) Write down a linear system of equations that describes the purchases (ii) Write your system of equations as a matrix-vector equation (iii) Is there a unique solution to (ii)? If so, find it and write down the cost of each item. If there is no unique solution, explain whether this is because the cashier made a mistake, or because you don’t have enough information. (a) You buy 3 apples and 2 bananas for $4. Your friend buys 1 apples and 2 bananas for $2. (b) You buy 2 carrots and 6 dates for $7. Your friend buys 3 dates and 1 carrot for $3.50. (c) You buy 1 eggplant and 2 fennel for $2.50. Your friend buys 4 eggplants and 8 fennel for $8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
1. Linear systems with 2 unknowns
You and a friend each purchase different quantities of the same items from a shop. In each of the cases (a)-(c)
below:
(i) Write down a linear system of equations that describes the purchases
(ii) Write your system of equations as a matrix-vector equation
(iii) Is there a unique solution to (ii)? If so, find it and write down the cost of each item. If there is no unique
solution, explain whether this is because the cashier made a mistake, or because you don’t have enough
information.
(a) You buy 3 apples and 2 bananas for $4. Your friend buys 1 apples and 2 bananas for $2.
(b) You buy 2 carrots and 6 dates for $7. Your friend buys 3 dates and 1 carrot for $3.50.
(c) You buy 1 eggplant and 2 fennel for $2.50. Your friend buys 4 eggplants and 8 fennel for $8.
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