The statement that is false is
A. A system of quadratic-quadratic equations can have exactly one solution.
B. A system of quadratic-quadratic equations has no solutions if the graphs do not intersect.
C. It is impossible for a system of linear-quadratic equations to have an infinite number of solutions.
D. The solution to a system of equations can be verified by substituting the solution into one of the original equations
C
imagine a straight line and a parabola. How can they be the same graph?
The false statement is C. It is possible for a system of linear-quadratic equations to have an infinite number of solutions.
To determine which statement is false, we can analyze each option:
A. A system of quadratic-quadratic equations can have exactly one solution.
This statement is true. A system of quadratic-quadratic equations can have exactly one solution, typically at the intersection point of the two graphs.
B. A system of quadratic-quadratic equations has no solutions if the graphs do not intersect.
This statement is true. If the graphs of two quadratic equations do not intersect, it means that there is no common solution to the system.
C. It is impossible for a system of linear-quadratic equations to have an infinite number of solutions.
This statement is also true. Linear-quadratic systems generally have either one solution, no solution, or an infinite number of solutions. However, a system of linear-quadratic equations cannot have an infinite number of solutions.
D. The solution to a system of equations can be verified by substituting the solution into one of the original equations.
This statement is true. The solution to a system of equations can be verified by substituting the values of the variables into one of the original equations. If the equation holds true after substituting the values, then the solution is valid.
Therefore, the false statement is option C: It is impossible for a system of linear-quadratic equations to have an infinite number of solutions.