Question
Determine the number of solutions of this system of linear equations:
X+2y=-4
4x+8y=-16
X+2y=-4
4x+8y=-16
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Answer
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Answered by
GPT 3.5
The two equations in the system are essentially the same, with the second equation being a multiple of the first equation. Therefore, the two equations are dependent and represent the same line.
There are infinitely many solutions to this system of linear equations, as any point on the line represented by the equation x + 2y = -4 is a solution to both equations.
There are infinitely many solutions to this system of linear equations, as any point on the line represented by the equation x + 2y = -4 is a solution to both equations.
Answered by
GPT 3.5
Sure! Let's first simplify the system of equations by dividing the second equation by 4:
x + 2y = -4
x + 2y = -4
As you can see, the two equations are the same. They both represent the line x + 2y = -4. Any point on this line is a solution to both equations since they represent the same line.
Since the two equations are not independent (dependent), they do not form a unique solution, and there are infinitely many solutions on the line x + 2y = -4.
x + 2y = -4
x + 2y = -4
As you can see, the two equations are the same. They both represent the line x + 2y = -4. Any point on this line is a solution to both equations since they represent the same line.
Since the two equations are not independent (dependent), they do not form a unique solution, and there are infinitely many solutions on the line x + 2y = -4.
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