Final Answer:
For the equation x+y=9, the completed table values are: x{0, 4, 9}, y{9, 5, 0}. For the equation 2x+3y=9, the completed table values are: x{0, 3, 9}, y{3, 1, 0}.
Step-by-step explanation:
For the equation x+y=9, completing the table with x-values {0, 4, 9} yields corresponding y-values {9, 5, 0}. Similarly, for the equation 2x+3y=9, using x-values {0, 3, 9} leads to corresponding y-values {3, 1, 0}.
Graphically representing x+y=9 and 2x+3y=21 involves plotting their respective lines on a graph. For x+y=9, the line has a y-intercept at 9 and an x-intercept at 9, forming a straight line. For 2x+3y=21, the equation simplifies to x+1.5y=7, which also forms a straight line with different intercepts.
To find the solution set where the two lines intersect, graphically overlay the lines representing x+y=9 and 2x+3y=21. The intersection point(s) indicate the x and y values that satisfy both equations simultaneously. In this case, the intersection point(s) obtained from the graph will yield the solution set for x and y values satisfying both equations.
Understanding how to represent equations graphically allows for visualizing their solutions and intersections, aiding in finding the simultaneous solutions for multiple equations and variables.