Which cannot describe a system of linear equations?
a) no solution
b) exactly two solutions
c) infinite solutions****
d) exactly one solution
To be honest I think the answer is C. Please Help!
C is true if the equations describe the same line. Then any point on one line is also on the others.
think a bit... graphs of linear equations are straight lines.
Can two straight lines intersect in two points?
Can three or more?
So? The answer would be?
To determine the correct answer, it's important to understand the concepts related to systems of linear equations.
A system of linear equations is a set of two or more equations with the same variables. The goal is to find the values of the variables that satisfy all the equations simultaneously.
Now let's consider the options:
a) No solution: This occurs when the system of equations has inconsistent equations, meaning there is no set of values that satisfies all the equations. In other words, the lines representing the equations do not intersect. This is a valid outcome for a system of linear equations.
b) Exactly two solutions: This implies that there are two distinct sets of values that satisfy the system of equations. It typically occurs when the lines representing the equations intersect at exactly one point. This is also a valid possibility for a system of linear equations.
c) Infinite solutions: This happens when all the equations in the system are equivalent or represent the same line. In this case, any set of values that satisfies one equation will automatically satisfy every other equation. This means that there are infinitely many values that can satisfy the system of equations.
d) Exactly one solution: This means that there is a unique set of values that satisfies the system of equations. The lines representing the equations intersect at a single point, and there is only one solution that satisfies all the equations.
Considering the definitions and possibilities mentioned above, it becomes clear that option c) "infinite solutions" cannot describe a system of linear equations. It is incorrect because a system of linear equations can either have no solution, exactly one solution, or exactly two solutions.