Final answer:
The question involves solving various systems of linear equations to find the values of x and y for each pair of equations provided. Methods such as substitution, elimination, or graphing can be utilized. Additionally, the plotting of the equation y = 9 + 3x illustrates the process of creating a graph from a linear equation.
Step-by-step explanation:
The question pertains to solving systems of linear equations, which are mathematical expressions representing straight lines, using coefficients of the variables x and y, along with given constants. Each system listed (such as 6x+y=-39 and 3x+2y=-15 or 8x+3y=4 and -7x+5y=-34) consists of two equations that need to be solved simultaneously to find the values of x and y. This can be done using methods such as substitution, elimination, or graphing.
For example, solving the system 3x-3y=-6 and -5x+6y=12, you could multiply the first equation by 2 and add it to the second equation to eliminate y. This yields an equation in x alone, which can be solved to find the value of x. Then, substitute the value of x back into either of the original equations to find y.
The structure of a table of x and y values and the graphing of the line are related to the equation y = 9 + 3x. To find the values of y corresponding to x, you plug various values of x into the equation. These (x, y) points are then plotted on a graph, and a line is drawn through them to represent the equation visually.