Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:
8x−2y=−4
4x−y=−2
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).
The correct statements are:
- There is exactly one solution to this system of linear equations and it is (2, 0).
- Solve this system by elimination since it is already in standard form and lined up nicely.
To find the solution to the system of equations, let's solve it step by step using the method of elimination.
1) Start with the given system of equations:
8x - 2y = -4 ...(1)
4x - y = -2 ...(2)
2) In order to eliminate one variable, we can multiply the second equation by 2, giving us:
8x - 2y = -4 ...(1)
8x - 2y = -4 ...(3)
3) Now, subtract equation (3) from equation (1) to eliminate the y variable:
(8x - 2y) - (8x - 2y) = (-4) - (-4)
0 = 0
4) The resulting equation, 0 = 0, means that the two equations are basically the same line. This indicates that the two lines are coincident or overlapping, hence there are infinitely many solutions.
Therefore, the correct statements are:
- There are infinite solutions to this system of linear equations.
Note: The option "There is exactly one solution to this system of linear equations and it is (2, 0)" is incorrect since the lines are not parallel and do not intersect at a single point.