Step 1: Graph the linear equation as a straight line in the xy plane:
To draw the graph, mark 2 points and draw a line between them. To make sure you have found the right points it is best to mark a third point. If there is no mistake all the points will be on the line. Which points to choose? Mark the points of intersection with the x-axis (y=0) and intersection with the y-axis (x=0) and then select a third point that is located between these two points.
For more details about graphing a line learn the graphic presentation of a linear function topic.
Step 2: Graph the quadratic equation as a parabola in the xy plane:
When we graph a quadratic function, we need to cover the vertex, the decreasing part and the increasing part. Plug some x values into the function to calculate their corresponding y values, plot the (x,y) coordinates in the xy plan and sketch a parabola through all the points.
For more details about graphing a parabola learn the graphing quadratic functions topic.
Step 3: See the coordinates of the intersection points of the line and the parabola:
The intersection can happen 0, 1 or 2 times, therefore a linear and quadratic system of equations can have 0, 1 or 2 solutions.
The graphs below show these 3 different possibilities of the solutions.