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 determine the correct statement(s) that describe the solution to the given system of equations, we can solve the system and examine the results.
The given system of equations:
8x - 2y = -4 ...(Equation 1)
4x - y = -2 ...(Equation 2)
We can use the method of elimination to solve this system. Multiply Equation 2 by 2 to make the coefficients of the y term in both equations equal:
8x - 2y = -4 ...(Equation 1)
8x - 2y = -4 ...(Equation 2)
Notice that the left sides of the equations are the same. This means that the two equations represent the same line. Therefore, the correct statement is:
These lines are parallel, so there is no solution to this system of linear equations.
By examining the system, we can see that the equations are dependent, meaning they represent the same line. Hence, there are infinite solutions to this system of linear equations.
The correct statement is:
- There is exactly one solution to this system of linear equations and it is (2, 0).