Can someone help me figure this out please?
when you solve a system of equations by the substitution method, how do you determine whether the system of equations is inconsistent?
thank you anyone
find the slope of each line. If they are the same, and not the same line, then they do not intersect -- no solution
Of course, I can help you with that! When you solve a system of equations by the substitution method, you can determine whether the system is inconsistent by looking at the results you obtained during the solving process.
To solve a system of equations by substitution, follow these steps:
1. Select one equation and solve it for one variable in terms of the other variable.
2. Substitute this expression into the other equation, replacing the variable.
3. Solve the resulting equation for the remaining variable.
4. Substitute this value back into one of the original equations to find the value of the first variable.
5. Check if the obtained values for both variables satisfy both original equations. If they do, the system is consistent and has a unique solution. If the obtained values do not satisfy one or both of the original equations, then the system is inconsistent.
The reason for this is that a consistent system of equations has one unique solution, where the graphs of the equations intersect. On the other hand, an inconsistent system of equations has no solution, where the graphs of the equations are parallel and do not intersect.
So, when you substitute the values of the variables back into the original equations, if one or both equations result in a contradiction (such as "0=2" or "3=4"), then the system is inconsistent.
I hope that helps! Let me know if you have any further questions.