When solving A system by graphing how can you tell if the solution is the equation of the line
When solving a system of equations by graphing, you can tell if the solution is the equation of the line by observing the point(s) of intersection on the graph.
Here's how to determine if the solution is the equation of the line:
1. Graph the system of equations: Start by graphing each equation on the same coordinate plane.
2. Identify the point(s) of intersection: Look for the point(s) where the graphs of the equations intersect each other. If there is no intersection, it means that the system probably has no solution or does not have a unique solution.
3. Substitute the point(s) into the equations: Take the coordinates of the point(s) of intersection and substitute them into each of the original equations. If the substituted values satisfy both equations, then the point(s) represent the solution(s) to the system.
4. Determine if the equation(s) match: Finally, check if the equation(s) you obtained by substituting the point(s) of intersection into the original equations match the given equation for the line. If they do, then the solution to the system represents the equation of the line.
Note that it is possible to have more than one point of intersection, in which case you will have multiple solutions. Additionally, if one of the equations is a multiple of the other, the system will have infinitely many solutions, and the equation of the line will be the same for both equations.
Always double-check your solution by substituting it back into the original equations to ensure accuracy.