Check all that apply. Select the statements) that correctly describes the solution to this system of equations:
8х - 2y = -4
4x-yー2
(2 points)
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 are infinite solutions 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).
• Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The correct statement is:
- Solve this system by elimination since it is already in standard form and lined up nicely.
To determine the solution to the system of equations, let's first solve it using the elimination method:
The given system of equations is:
8x - 2y = -4 --> Equation (1)
4x - y = 2 --> Equation (2)
To eliminate the y term, we can multiply Equation (2) by -2 and add it to Equation (1):
-2 * (4x - y) = -2 * 2
-8x + 2y = -4
Now, we add Equation (1) and the modified Equation (2):
(8x - 2y) + (-8x + 2y) = -4 + 2
0 = -2
The equation 0 = -2 is not true, and therefore, the system of equations is inconsistent. This means that there is no solution to this system of linear equations.
Hence, the correct statement is:
These lines are parallel, so there is no solution to this system of linear equations.
To find the solution to the system of equations:
8x - 2y = -4
4x - y - 2
Firstly, let's check the given options one by one:
1. Solve this system by elimination since it is already in standard form and lined up nicely.
This option suggests solving the system by elimination. However, the system is not written correctly for elimination as the second equation should have an equal sign instead of a hyphen.
2. There is exactly one solution to this system of linear equations and it is (2, 0).
To check if this statement is true, we need to substitute the values of x and y into both equations of the system and see if they satisfy both equations.
For the first equation, when x = 2 and y = 0, we have:
8(2) - 2(0) = -4
16 - 0 = -4
16 = -4
The equation is not satisfied, so this statement is not true.
3. There are infinite solutions to this system of linear equations.
To check if this statement is true, we need to determine if the two equations represent the same line. We can do this by rearranging both equations to slope-intercept form (y = mx + b).
The first equation:
8x - 2y = -4
-2y = -8x - 4
y = 4x + 2
The second equation:
4x - y = 2
-y = -4x + 2
y = 4x - 2
By comparing the equations, we can see that they have the same slope (4) and different y-intercepts (2 and -2). This means that the lines are parallel and never intersect. Therefore, there is no solution, and this statement is true.
4. There is exactly one solution to this system of linear equations and it is (0, -2).
Similar to the second option, we can substitute the values of x and y into both equations and check if they satisfy:
For the first equation:
8(0) - 2(-2) = -4
0 + 4 = -4
4 = -4
The equation is not satisfied, so this statement is not true.
5. Solve this system by substitution since one of the variables is defined by the other without having to do any math.
This option suggests solving the system by substitution. However, it does not provide any specific information on how to proceed with the substitution process.
Based on the analysis, the correct statement is:
- There are infinite solutions to this system of linear equations.
This means that the lines representing the equations are parallel and never intersect.