Follow the step-by-step procedure.
Start with either one of your equations.
Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier.
Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results.
Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y).
Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis.
Step 5. Repeat steps 1 through 4 with a different value for x.
Step 6. Draw a line across your graph that passes through the two points that you plotted.
Step 7. Repeat steps 1 through 6 using the other equation.
The point where the lines intersect is the solution, because the coordinates of that point will satisfy (read: make true) both of your equations. You need to determine, by inspection of the graph, what the coordinates of that point are and report your answer as an ordered pair, (x,y), using those coordinates. To check your answer, you should substitute this set of coordinates into each of your original equations and verify that you have a true statement for each of the equations.
If both lines graph to the same line, then the solution set is infinite, i.e. every ordered pair that satisfies one equation will satisfy the other. If the lines are parallel, then the solution set is empty.
Definitions:
A consistent system has at least one solution. (It may have more than one)
An inconsistent system has zero solutions.
An independent system has exactly one solution.
A dependent system has an infinite number of solutions.
Graphical interpretation.
The graph of a consistent and independent system is a pair of straight lines that intersect in one point.
The graph of a consistent and dependent systme is a pair of straight lines that are superimposed on each other, i.e. they are the same line.
The graph of an inconsistent system is a pair of parallel lines.
John
My calculator said it, I believe it, that settles it
