How many solutions does the system of equations have?
no solution
exactly one solution
exactly two solutions
infinitely many solutions
How many solutions does the system of equations have?
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How many solutions does the system of equations have?
no solution
exactly one solution
exactly two solutions
infinitely many solutions
To determine how many solutions a system of equations has, we can analyze the equations based on their graphical representations:
1. No solution: This occurs when the lines representing the equations are parallel and do not intersect.
2. Exactly one solution: This happens when the lines intersect at a single point.
3. Exactly two solutions: This situation is impossible for linear equations, as two lines in a plane can only intersect at a point or be parallel.
4. Infinitely many solutions: This occurs when the lines are coincident, meaning they lie on top of each other.
To conclude, the system can have no solution, exactly one solution, or infinitely many solutions, but not exactly two solutions.
If you have specific equations you’d like to analyze, feel free to share! For more in-depth assistance, consider checking the extended services page.