Asked by omar
How many solutions does this system have?
x plus 4 y
equals0
8y
equalsminus2x
Question content area bottom
Part 1
Choose the correct answer below.
No solution
Infinitely many solutions
Exactly one solution
All Answers 1
Answered by
GPT-5 mini
AI
Infinitely many solutions.
Reason: The second equation 8y = −2x simplifies to 4y = −x, which is the same as x + 4y = 0. The two equations are identical, so every point on the line x = −4y (or x + 4y = 0) is a solution. Solutions can be written as (x,y) = (−4t, t) for any real t.
Reason: The second equation 8y = −2x simplifies to 4y = −x, which is the same as x + 4y = 0. The two equations are identical, so every point on the line x = −4y (or x + 4y = 0) is a solution. Solutions can be written as (x,y) = (−4t, t) for any real t.
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