Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:

Question

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 mat

Answer 1

To determine the correct statements about the system of equations:

1. Equations:

   • \(8x - 2y = -4\)
   • \(4x - y = -2\)

2. Standard Form: Both equations are already in standard form, so elimination or substitution can be used.

3. Elimination: To apply elimination:

   • Multiply the second equation by 2 to align coefficients of \(y\):
   • \(2(4x - y) = 2(-2)\) → \(8x - 2y = -4\)

   Now, we have:

   • \(8x - 2y = -4\) (first equation)
   • \(8x - 2y = -4\) (modified second equation)

   Since both equations are identical, this indicates that they represent the same line, leading to infinite solutions.

4. Checking the solutions:

   • The first statement about solving it via elimination is correct, as it is in standard form.
   • The statement that there are infinite solutions to this system is also valid since both equations represent the same line.
   • The statements about having exactly one solution or lines being parallel are incorrect, as they contradict the fact that there are infinite solutions.

5. Final assessment:

   • Statements that correctly describe the solution:
     • Solve this system by elimination since it is already in standard form and lined up nicely.
     • There are infinite solutions to this system of linear equations.

Thus, the correct responses are:

• Solve this system by elimination since it is already in standard form and lined up nicely.
• There are infinite solutions to this system of linear equations.

Answer 2

pick 2 from the answers

Answer 3

Based on the analysis of the system of equations, the two correct statements are:

1. Solve this system by elimination since it is already in standard form and lined up nicely.
2. There are infinite solutions to this system of linear equations.

These statements accurately describe the solution to the given system.