A system of equations is a set of two or more equations that contain multiple variables and are meant to be solved simultaneously. The solution to a system of equations is the values of the variables that make all of the equations true.
A system of equations has infinite solutions if the equations are dependent, meaning that one equation can be obtained from the other by performing basic algebraic operations. This essentially means that the equations are expressing the same relationship and therefore have an infinite number of solutions.
If a system of equations has infinite solutions, the best way to solve it is to choose a value for one of the variables and then solve for the remaining variables. This will give you one possible solution, but there will still be an infinite number of solutions because you can choose a different value for the first variable and get a different solution.
No, a system of equations cannot have both infinite and no solutions. If a system of equations has infinite solutions, it means that the equations are dependent and therefore have an infinite number of solutions. If a system of equations has no solutions, it means that the equations are inconsistent and there is no possible set of values for the variables that make all of the equations true.
Graphing a system of equations with infinite solutions can be done by graphing each equation on the same coordinate plane and looking for points of intersection. Since there are an infinite number of solutions, there will be multiple points of intersection, forming a line. The equations will have the same slope and y-intercept, and therefore will be parallel lines.