Consistent lines intersect at point which represents the unique solution of the system of linear equations in two variables. Algebraically, if then, the linear equations' pair is consistent.
Inconsistent lines are parralel are inconsistent

Consistent and Inconsistent Pairs of Linear Equations

Consistent and inconsistent are terms used to describe pairs of linear equations in two variables. A pair of linear equations is said to be consistent if it has at least one solution that satisfies both equations. On the other hand, a pair of linear equations is said to be inconsistent if it has no solution that satisfies both equations.

Consistent Pairs of Linear Equations

A pair of linear equations is consistent if it has at least one solution that satisfies both equations. This means that the two lines represented by the equations will intersect at a point. There are three types of consistent pairs of linear equations:

1. Unique Solution - When the two lines intersect at one point, there is only one solution to the equations.

2. Infinitely Many Solutions - When the two lines coincide, there are infinitely many solutions to the equations.

3. Same Slope, Different y-intercepts - When the two lines are parallel, there are no solutions to the equations.

Inconsistent Pairs of Linear Equations

A pair of linear equations is inconsistent if it has no solution that satisfies both equations. This means that the two lines represented by the equations do not intersect. There is only one type of inconsistent pair of linear equations:

1. Same Slope, Same y-intercept - When the two lines are parallel and have the same y-intercept, there are no solutions to the equations.

Conclusion

In conclusion, consistent and inconsistent are terms used to describe pairs of linear equations in two variables. A pair of linear equations is consistent if it has at least one solution that satisfies both equations, while a pair of linear equations is inconsistent if it has no solution that satisfies both equations. It is important to understand these terms when solving problems involving linear equations.