To determine whether there is an ordered pair that is a solution to the linear equations describing two lines, we need to check if the lines intersect. The lines will intersect if they are not parallel or coincident.
Here’s how you can analyze it:
-
Find the equations of the lines: If the equations are provided, rewrite them in slope-intercept form (y = mx + b) or in standard form (Ax + By = C).
-
Compare slopes:
- If the slopes (m) of both lines are equal and the y-intercepts (b) are different, the lines are parallel and there is no solution (no intersection).
- If the slopes are equal and the y-intercepts are the same, the lines coincide (are the same line), and there are infinitely many solutions (every point on the line is a solution).
- If the slopes are different, the lines will intersect at exactly one point, which means there is exactly one ordered pair that is the solution.
If you can provide the specific equations of the lines, I can help you determine if there is an ordered pair that is a solution. Otherwise, without further information on the lines, the answer would be "It depends" on the specific lines in question.