Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:

B: there is exactly one solution to this system of linear equations and it is (2,0)

The correct statement(s) that describe the solution to this system of equations are:

B: There is exactly one solution to this system of linear equations, and it is (2,0).
F: Solve this system by substitution since one of the variables is defined by the other without having to do any math.

To find the solution to this system of equations, we need to analyze the given equations and determine their relationship to each other. Let's go through each option and explain the process.

A: Solve this system by elimination since it is already in standard form and lined up nicely.
In this case, we would look for a way to eliminate one variable by multiplying one or both equations to create matching coefficients. However, this system is not ready for elimination since the coefficients of the variables do not match.

B: There is exactly one solution to this system of linear equations, and it is (2, 0).
To confirm if this statement is correct, we need to solve the system of equations. One approach is to use the method of substitution or elimination.

Using the elimination method, we can multiply the second equation by 2 to obtain:
8x - 2y = -4
8x - 2y = -4

Now, we have two equations that are identical, meaning the two lines coincide. Therefore, there are infinitely many solutions to this system of equations rather than exactly one solution.

C: There are infinite solutions to this system of linear equations.
This statement is correct based on our explanation in option B. The two lines coincide, indicating that there are infinitely many solutions.

D: These lines are parallel, so there is no solution to this system of linear equations.
This statement is incorrect because, as we determined in option B, the two lines coincide, indicating infinitely many solutions rather than no solution.

E: There is exactly one solution to this system of linear equations, and it is (0, -2).
This statement is incorrect since the solution we found in option B was (2, 0), not (0, -2). Therefore, this option does not correctly describe the solution.

F: Solve this system by substitution since one of the variables is defined by the other without having to do any math.
In this case, the second equation can be rewritten as y = 4x + 2. We can then substitute this expression into the first equation to solve for x:
8x - 2(4x + 2) = -4
Simplifying the equation gives:
8x - 8x - 4 = -4
-4 = -4

This equation is true, indicating that the two equations are dependent. As a result, there are infinitely many solutions to the system.

Based on the explanations provided, options C and F correctly describe the solution to this system of equations.