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 need to consider their relationship:
1. No solution: This occurs when the equations represent parallel lines that never intersect.
2. Exactly one solution: This happens when the two lines intersect at a single point, meaning they have different slopes.
3. Exactly two solutions: This situation is not possible in a system of linear equations, as two linear equations can either intersect at one point, be parallel (no solutions), or be identical (infinitely many solutions).
4. Infinitely many solutions: This occurs when the two equations represent the same line, meaning there are countless points of intersection.
To find the solution type, analyze the equations’ slopes and intercepts. If you have specific equations in mind, feel free to share them for a more focused analysis!