Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:8x−2y=−4 4x−y=−2 (2 points)Responses Solve this system by elimination since it is already in standard form and lined up nicely.Solve this system by elimination since it is already in standard form and lined up nicely.There is exactly one solution to this system of linear equations and it is (2, 0).There is exactly one solution to this system of linear equations and it is (2, 0).There are infinite solutions to this system of linear equations.There are infinite solutions to this system of linear equations.These lines are parallel, so there is no solution to this system of linear equations.These lines are parallel, so there is no solution to this system of linear equations.There is exactly one solution to this system of linear equations and it is (0, -2).There is exactly one solution to this system of linear equations and it is (0, -2).Solve this system by substitution since one of the variables is defined by the other without having to do any math.Solve this system by substitution since one of the variables is defined by the other without having to do any math.

Question

GPT-4o mini · Answer

To determine which statements correctly describe the solution to the given system of equations, we should first solve the system:

The system of equations is: \[ 8x - 2y = -4 \quad \text{(1)} \] \[ 4x - y = -2 \quad \text{(2)} \]
To solve by elimination, we can manipulate one of the equations to align the coefficients. Let’s multiply equation (2) by 2, so we can eliminate \(y\): \[ 2(4x - y) = 2(-2) \implies 8x - 2y = -4 \quad \text{(which is exactly equation (1))} \]

Now, we see that both equations are identical, meaning they describe the same line. Therefore, there are infinite solutions to this system of equations.

Given this analysis, the correct statements from your list are:

There are infinite solutions to this system of linear equations.
Solve this system by elimination since it is already in standard form and lined up nicely.

Thus, the statements "There are infinite solutions to this system of linear equations" and "Solve this system by elimination since it is already in standard form and lined up nicely" are correct.