Suppose you find that two linear equations are true when x = -2 and y = 3. What can you conclude about the graphs of the equations?
the lines intersect at (-2,3)
If the two linear equations are true when x = -2 and y = 3, it means that (-2, 3) is a common solution to both equations. This implies that the graphs of the equations intersect at the point (-2, 3).
Furthermore, since a linear equation represents a straight line, we can conclude that the two graphs will intersect at that point (-2, 3). Thus, the lines represented by the equations will cross or intersect each other at the given point.
To determine what can be concluded about the graphs of two linear equations when specific values of x and y satisfy both equations, follow these steps:
1. Plug in the given values of x and y (-2 and 3, respectively) into both equations.
2. Calculate the left-hand side and right-hand side of each equation separately for this particular point.
3. If the calculated values are equal for both equations, it means that the point (-2, 3) lies on the graphs of both equations.
4. Repeat this process for multiple other points to verify if they also satisfy both equations.
5. If all the tested points satisfy both equations, it indicates that the graphs of the equations are the same line.
6. Conversely, if there exists at least one point that does not satisfy both equations, it means the graphs of the equations are different and do not intersect at that point.
In summary, if two linear equations are true when x = -2 and y = 3, it can be concluded that these equations represent the same line.