Final answer:
To solve the system of equations, graph both lines, find their intersection, and determine the x and y coordinates of the solution. This solution corresponds to the point satisfying both equations.
Step-by-step explanation:
To solve the system of equations given by y = 3x + 9 and y = -x - 9, we'll first graph these equations on a coordinate plane. The first equation, y = 3x + 9, represents a line with a y-intercept of 9 and a slope of 3. This means for every increase of 1 in x, y increases by 3. To graph this line, we can use a table of values and plot points to draw the line.
The second equation, y = -x - 9, has a y-intercept of -9 and a slope of -1, indicating a decrease in y by 1 for every increase in x by 1. Using table values, we plot this line on the same graph.
To find the solution to this system of linear equations, we look for the point where the two lines intersect. This point of intersection represents the x and y values that satisfy both equations simultaneously. After plotting these lines, we conclude the x-coordinate and y-coordinate of the solution to the system, and determine which of the given statements about the solution are true.