Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:
8х - 2y = -4
4x-yー2
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 statement "These lines are parallel, so there is no solution to this system of linear equations" correctly describes the solution to this system of equations.
To solve this system of equations:
1. Start with the given equations:
- 8x - 2y = -4
- 4x - y = 2
2. We can solve the system using the method of elimination or substitution. Let's use substitution since one of the variables is defined by the other without having to do any math.
3. From the second equation, we can isolate y:
- 4x - y = 2
- y = 4x - 2
4. Now we substitute the value of y into the first equation:
- 8x - 2(4x - 2) = -4
5. Simplify the equation:
- 8x - 8x + 4 = -4
- 4 = -4
6. The equation -4 = -4 is contradictory, meaning there is no possible solution that satisfies both equations.
Therefore, the correct statement is: These lines are parallel, so there is no solution to this system of linear equations.
To check which statement(s) correctly describe the solution to the system of equations, let's solve the system:
8x - 2y = -4 (Equation 1)
4x - y - 2 = 0 (Equation 2)
To solve the system using the elimination method, we can multiply Equation 2 by 2 to make the coefficients of the y term the same:
2(4x - y - 2) = 2(0)
8x - 2y - 4 = 0 (Equation 3)
Now we can subtract Equation 3 from Equation 1 to eliminate the y variable:
(8x - 2y) - (8x - 2y - 4) = -4 - 0
8x - 2y - 8x + 2y + 4 = -4
0 + 4 = -4
4 ≠ -4
Since 4 is not equal to -4, this means that the system of equations is inconsistent, and there are no solutions. Therefore, the correct statement is:
These lines are parallel, so there is no solution to this system of linear equations.
This is wrong there is more than one answer
My apologies for the incorrect response. Let's re-evaluate the system of equations:
Equation 1: 8x - 2y = -4
Equation 2: 4x - y = 2
To solve the system, we will use the method of elimination:
Multiply Equation 2 by -2:
-2(4x - y) = -2(2)
-8x + 2y = -4 (Equation 3)
Now, add Equation 1 and Equation 3:
(8x - 2y) + (-8x + 2y) = -4 + (-4)
0 = -8
The equation 0 = -8 is a contradiction, indicating that the system of equations has no solution.
Therefore, the correct statement is:
These lines are parallel, so there is no solution to this system of linear equations.