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.
There is exactly one solution to this system of linear equations and it is (2, 0).
how many solutions are ther
There is exactly one solution to this system of linear equations.
The correct statement(s) that describe the solution to this system of equations are:
- 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 determine the correct statement(s) that describe the solution to the given system of equations, let's go through the options one by one and see how we can solve the system.
Option 1: Solve this system by elimination since it is already in standard form and lined up nicely.
This is a valid approach. If the system is already in standard form (ax + by = c) and the coefficients are aligned nicely, elimination can be used to solve the system.
Option 2: There is exactly one solution to this system of linear equations and it is (2, 0).
To determine if this is true, we need to solve the system and see if it results in a single unique solution of (2, 0).
Option 3: There are infinite solutions to this system of linear equations.
To determine if this is true, we need to solve the system and see if it results in infinitely many solutions.
Option 4: These lines are parallel, so there is no solution to this system of linear equations.
To determine if this is true, we can compare the slopes of the two equations. If the slopes are equal, the lines are parallel, and there is no solution.
Option 5: There is exactly one solution to this system of linear equations and it is (0, -2).
To determine if this is true, we need to solve the system and see if it results in a single unique solution of (0, -2).
Option 6: Solve this system by substitution since one of the variables is defined by the other without having to do any math.
If one variable is defined by the other in one of the equations, substitution can be used to solve the system.
Now, let's actually solve the system of equations to find the correct statement(s).
The given equations are:
1) 8x - 2y = -4
2) 4x - y = -2
To eliminate one variable, we can multiply equation (2) by 2:
2 * (4x - y) = 2 * (-2)
8x - 2y = -4
We can see that equation (2) is essentially the same as equation (1). Therefore, these equations represent the same line, and there are infinitely many solutions to this system.
So, the correct statement(s) would be:
- There are infinite solutions to this system of linear equations.
Note: The other options described different approaches to solve the system, but they are not applicable in this case since the given system of equations represents the same line.