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 relationships between the equations.
– No solution occurs when the equations represent parallel lines that never intersect.
– Exactly one solution happens when the lines intersect at a single point, indicating the equations are independent.
– Exactly two solutions is typically not possible for a system of linear equations in two variables, as lines can only intersect at one point or be parallel.
– Infinitely many solutions occur when the equations represent the same line, meaning they are dependent.
You would need to evaluate the specific equations to categorize them into one of these four cases. If you have two equations, try plotting them or calculating their slopes to find out how many solutions exist. If you need more detailed exploration, consider checking the extended services available for deeper analysis.