Question

Your friend, Taylor, missed class today and needs some help identifying solutions to systems. Explain to Taylor how to find the solution(s) of any system using its graph.

will my answer be correct:
to find the solution(s) of any system using the graph you have to graph both equations in the same coordinate system. plug the values for x and y into the equation to see if they work for the equation. the solution has to be the point where the two lines intersect.

Answer 1

If you want to find the solution of any system of equations graphically,

1. Plot the graph of both the equation in the same coordinate system.

2. Find the point of intersection.

Three cases comes into consideration, when you plot two lines in same coordinate system

1. If the two lines intersect, they have one point in Common.

2. The two lines may not intersect, and when they do not intersect, chances are

(a) The two lines are parallel, means they never touch each other when produced indefinitely in both the direction.

(b) The two lines may be coincident, means equation of both the lines are same, and one line completely covers the other line and vice versa and have infinite number of solutions.

Your answer is correct ,apart from the statement that you have asserted→→:plug the values for x and y into the equation to see if they work for the equation.

Why i am saying this, if the two lines have one point of intersection, it means that point is solution of the system of equation satisfying both the equations. So, you don't need to plug values of x and y into the equation to check, if you are solving graphically.