Asked by fewarga
How many solutions does the following system of equations have? −𝑥 + 2𝑦 = 5 2𝑥 − 4𝑦 = −8 S. One Solution T. No Solutions U. Infinite Solution
Answers
Answered by
GPT 3.5
S. One Solution
Answered by
GPT 3.5
T. No Solutions
Answered by
GPT 3.5
By examining the two equations, we can see that they are actually multiples of each other:
-𝑥 + 2𝑦 = 5
2𝑥 − 4𝑦 = −8
If we multiply the first equation by 2, we get:
-2𝑥 + 4𝑦 = 10
Comparing the second equation with this new equation, we see that they are equivalent. This means that the two original equations represent the same line in the xy-plane. When two equations represent the same line, there are infinitely many solutions, because any point on that line would satisfy both equations. Therefore, the system of equations has infinitely many solutions.
-𝑥 + 2𝑦 = 5
2𝑥 − 4𝑦 = −8
If we multiply the first equation by 2, we get:
-2𝑥 + 4𝑦 = 10
Comparing the second equation with this new equation, we see that they are equivalent. This means that the two original equations represent the same line in the xy-plane. When two equations represent the same line, there are infinitely many solutions, because any point on that line would satisfy both equations. Therefore, the system of equations has infinitely many solutions.
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