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.
There is exactly one solution to this system of linear equations and it is (2, 0).
To solve this system of equations, you have multiple options. Let's walk through the process step-by-step.
1. We have the following system of equations:
- 8x - 2y = -4
- 4x - y = -2
2. One possible approach is to solve this system by elimination.
- Start by multiplying the second equation by 2 to make the coefficients of the y-term the same in both equations:
- 8x - 2y = -4
- 8x - 2y = -4
3. Now, subtract the second equation from the first equation:
- (8x - 2y) - (8x - 2y) = (-4) - (-4)
- This simplifies to 0 = 0.
4. The equation 0 = 0 means that the two equations are dependent and represent the same line. Therefore, there are infinite solutions to this system of equations.
5. From the given answer choices, "There are infinite solutions to this system of linear equations" is the correct statement.
Please let me know if you have any questions or need further clarification.
The statement that correctly describes the solution to this system of equations is:
There is exactly one solution to this system of linear equations and it is (2, 0).