Which best describes a system of equations that has no solution
A system of equations that has no solution is one where the equations are inconsistent and cannot be satisfied simultaneously. This means that the graphs of the equations do not intersect and are parallel to each other.
A system of equations that has no solution is called an inconsistent system. This occurs when the lines represented by the equations are parallel and do not intersect. In other words, the lines are distinct and do not have any common points.
A system of equations that has no solution is generally described as "inconsistent" or "contradictory". This means that the equations in the system cannot be satisfied simultaneously because they represent contradictory statements. In other words, there are no values for the variables that can make all the equations true at the same time.
To determine if a system of equations has no solution, you can do the following:
1. Write down all the equations in the system.
2. Analyze the coefficients and constants in each equation.
3. Compare the equations and look for any inconsistencies or contradictions.
4. Try to solve the system using algebraic methods, such as substitution or elimination.
5. If you reach a point where the equations contradict each other or you cannot find any values that satisfy all the equations, then the system has no solution.
For example, consider the following system of equations:
Equation 1: 2x - 3y = 7
Equation 2: 4x - 6y = 11
To solve this system, we can multiply Equation 1 by 2:
Equation 1 (after multiplication): 4x - 6y = 14
Now we can see that Equation 2 and the modified Equation 1 are identical. This means that the two equations represent the same line. Since the lines are identical, they intersect at every point and have infinitely many solutions, rather than no solution.
Therefore, a system of equations with no solution would have contradictory equations where the lines never intersect or have inconsistent coefficients/variables.