City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −3° C. The following system of equations models this scenario: 4x = 8 3y x − 2y = −3 What was the temperature of City A and City B on that day? City A was 5° C, and City B was 4° C. City A was 3° C, and City B was −1° C. City A was 8° C, and City B was −3° C. City A was 5° C, and City B was −5° C.
4x = 8 + 3y x - 2y = -3 "four times the temperature of City A was 8° C more than three times the temperature of City B." looking at the first equation, since x is being multiplied by 4 (corresponding to "four times the temperature of city a"), and being set equal to "8 + 3y" (corresponding to "8 more than three times the temperature of city B) we can reasonably conclude that x represents city A's temperature and y correspondings to city B's temperature
from there, we can solve the system of equations for x and y 4x = 8 + 3y x - 2y = -3 let's get both of them in ax + by = c form we can do this by taking the first equation and subtracting 3y from both sides 4x -3y = 8 x - 2y = -3 now, we can try to eliminate either the x's or the y's. notice how we have 4x in the first equation and x in the second equation. therefore, we can multiply the second equation by 4. you will end up with a 4x term in the second equation. since you now have 4x in both equations, you can subtract the two equations to eliminate the x terms. once you only have y terms, simply solve for y. that's your temperature of city B. since all the answer choices have different temperatures for city B, you can simply find the answer choice that matches your calculations.
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