What is an example of a system of equations that has infinitely many solutions?
If by a system of equations you want two “different” equations with infinitely many points (solutions) in common you could take any linear equation like the one Hamilton gave you y = x + 1 and multiply it by 2 to get 2y = 2x + 2.
How do you tell if a system of equations has no solution or infinitely many?
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
How can a system of three equations in three variables has infinitely many solutions complete the explanation?
An infinite number of solutions can result from several situations. The three planes could be the same, so that a solution to one equation will be the solution to the other two equations. All three equations could be different but they intersect on a line, which has infinite solutions.
How do you know if a problem has infinite solutions?
When a problem has infinite solutions, you’ll end up with a statement that’s true no matter what. For example: 3=3 This is true because we know 3 equals 3, and there’s no variable in sight. Therefore we can conclude that the problem has infinite solutions. You can solve this as you would any other equation.
What does it mean when a system has infinitely many solutions?
Systems with Infinitely Many Solutions There is always a possibility that a system of equations has infinite solutions. If the equations in your system are the same, then there are infinite solutions.
How do you know if there are infinitely many solutions?
Equations with an infinite number of solutions If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.
How do you find infinitely many solutions?
If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.