Check all that apply. Select the statements that correctly describes the solution to this system of equations:
8x-2y=-4
4x-y=-2
A. Solve this system by elimination, since it is already in standard form and lined up nicely.
B. There is exactly one solution to this system of line and it is (2,0)
C. There are infinite solutions to the system of linear equations
D. These lines are parallel, so there is no solution to this system of linear equations.
E. There is exactly one solution to this system of linear equations, and it is (0,-2)
F. Solve this substitution since one of the variables is defined by the other, without having to do any math
B. There is exactly one solution to this system of line and it is (2,0)
Is B the only one that correctly describes the solution to those system of equations?
Yes, B is the only statement that correctly describes the solution to this system of equations.
To determine which statements correctly describe the solution to the system of equations, let's analyze the given equations first:
Equation 1: 8x - 2y = -4
Equation 2: 4x - y = -2
We can solve this system by either elimination or substitution. Let's go through the options one by one:
A. Solve this system by elimination, since it is already in standard form and lined up nicely.
This statement is incorrect. While the system is in standard form, it requires some manipulation before we can solve it using the elimination method.
B. There is exactly one solution to this system of line and it is (2,0).
C. There are infinite solutions to the system of linear equations.
D. These lines are parallel, so there is no solution to this system of linear equations.
E. There is exactly one solution to this system of linear equations, and it is (0,-2).
These statements are incorrect. To determine the validity of these options, we need to solve the system of equations.
F. Solve this substitution since one of the variables is defined by the other, without having to do any math.
This statement is incorrect. The equations do not provide a direct relationship between the variables, requiring us to perform calculations.
Now, let's solve the system using either elimination or substitution to determine the accurate option:
Using the elimination method, we can multiply Equation 2 by 2 to make the coefficients of y the same:
Equation 1: 8x - 2y = -4
Equation 2: 8x - 2y = -4
Now, subtract Equation 2 from Equation 1:
(8x - 2y) - (8x - 2y) = (-4) - (-4)
0 = 0
We can see that both equations are the same, meaning they represent the same line. This indicates that there are infinite solutions to the system of equations.
Therefore, the correct statement is:
C. There are infinite solutions to the system of linear equations.
To find the solution using the elimination method without evaluating the equations, they should be simplified and lined up nicely.