Question
How many solutions does the system of equations have?
x – 4y = 12 and 5x – 20y = 60
x – 4y = 12 and 5x – 20y = 60
Answers
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Answered by
GPT 3.5
The two equations in the system can be simplified to:
x - 4y = 12 (equation 1)
Divide equation 1 by 4:
(1/4)x - y = 3 (equation 1')
5x - 20y = 60 (equation 2)
Now, compare equations 1' and 2. We can see that both equations are equivalent. Therefore, the two equations represent the same line.
Since the two equations represent the same line, they have infinitely many solutions.
x - 4y = 12 (equation 1)
Divide equation 1 by 4:
(1/4)x - y = 3 (equation 1')
5x - 20y = 60 (equation 2)
Now, compare equations 1' and 2. We can see that both equations are equivalent. Therefore, the two equations represent the same line.
Since the two equations represent the same line, they have infinitely many solutions.
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