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

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.

CHOOSE ALL THAT APPLY

Answer 1

To solve the system of equations:

1. 8x - 2y = -4
2. 4x - y = -2

Let's first work through the elimination method.

Step 1: Adjust the equations

We can multiply the second equation by 2 to align the coefficients of \(y\):

\[ 2(4x - y) = 2(-2) \] \[ 8x - 2y = -4 \]

This produces:

1. 8x - 2y = -4 (remains the same)
2. 8x - 2y = -4 (from multiplying the second equation)

Both equations become identical, which indicates that they represent the same line.

Conclusion

Since both equations are identical, there are infinite solutions along the line represented by these equations.

Now we evaluate each statement given:

1. There is exactly one solution to this system of linear equations and it is (2, 0). (Incorrect, there are infinitely many solutions)
2. There are infinite solutions to this system of linear equations. (Correct)
3. These lines are parallel, so there is no solution to this system of linear equations. (Incorrect, they are not parallel; they are the same line)
4. There is exactly one solution to this system of linear equations and it is (0, -2). (Incorrect, there are infinitely many solutions)
5. Solve this system by substitution since one of the variables is defined by the other without having to do any math. (Incorrect, both equations are identical, but substitution isn't straightforward)

Therefore, the correct selections are:

• There are infinite solutions to this system of linear equations.