Choose ALL that apply. Select the statement(s) that correctly describes the solution to this system of equations:
8x−2y=−4
4x−y=−2
1 Solve this system by elimination since it is already in standard form and lined up nicely.
2 There is exactly one solution to this system of linear equations and it is (2, 0).
3 There are infinite solutions to this system of linear equations.
4 These lines are parallel, so there is no solution to this system of linear equations.
5 There is exactly one solution to this system of linear equations and it is (0, -2).
6 Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The correct statements are:
2 There is exactly one solution to this system of linear equations and it is (2, 0).
6 Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The correct statements are:
2) There is exactly one solution to this system of linear equations and it is (2, 0).
4) These lines are parallel, so there is no solution to this system of linear equations.
6) Solve this system by substitution since one of the variables is defined by the other without having to do any math.
To solve this system of equations, we need to find the values of x and y that satisfy both equations. Let's go through each statement to determine which one(s) correctly describe the solution.
1. Solve this system by elimination since it is already in standard form and lined up nicely.
Elimination is a valid method to solve this system, but we need to check if it leads to a solution.
2. There is exactly one solution to this system of linear equations and it is (2, 0).
To check this solution, let's substitute x = 2 and y = 0 into both equations:
For the first equation: 8(2) - 2(0) = 16
For the second equation: 4(2) - 0 = 8
As these values do not satisfy the given equations, statement 2 is not correct.
3. There are infinite solutions to this system of linear equations.
For two lines to have infinite solutions, they must be coincident or overlapping. To determine this, we can compare the slopes of the lines.
The slopes of the lines given by the two equations are 8/2 = 4 and 4/1 = 4, respectively. Since the slopes are equal, the lines are coincident or overlapping, and statement 3 is correct.
4. These lines are parallel, so there is no solution to this system of linear equations.
To check if the lines are parallel, we need to compare their slopes. As the slopes are equal, the lines are not parallel. Therefore, statement 4 is incorrect.
5. There is exactly one solution to this system of linear equations and it is (0, -2).
To check this solution, let's substitute x = 0 and y = -2 into both equations:
For the first equation: 8(0) - 2(-2) = 4
For the second equation: 4(0) - (-2) = 2
As these values do not satisfy the given equations, statement 5 is not correct.
6. Solve this system by substitution since one of the variables is defined by the other without having to do any math.
Neither of the variables in this system is defined by the other, so substitution is not needed. Therefore, statement 6 is incorrect.
To summarize, the correct statements describing the solution to this system of equations are:
- There are infinite solutions to this system of linear equations. (Statement 3)