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

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 math.

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1 answer

To analyze the system of equations:

  1. Equations: \[ 8x - 2y = -4 \quad \text{(1)} \] \[ 4x - y = -2 \quad \text{(2)} \]

First, I will rearrange equation (1) to see if it can be simplified or transformed to match the form of equation (2).

  • Simplifying (1): \[ 8x - 2y = -4 \implies 4x - y = -2 \quad \text{(after dividing the whole equation by 2)} \]

This shows that both equations represent the same line.

Based on this analysis, we can evaluate the given statements:

  1. Solve this system by elimination since it is already in standard form and lined up nicely.

    • This can apply since the equations are in standard form.

  2. There is exactly one solution to this system of linear equations and it is (2, 0).

    • This is incorrect since the equations represent the same line.

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

    • This is correct because both equations represent the same line.

  4. These lines are parallel, so there is no solution to this system of linear equations.

    • This is incorrect; the lines are not parallel; they are the same.

  5. There is exactly one solution to this system of linear equations and it is (0, -2).

    • This is incorrect.

  6. Solve this system by substitution since one of the variables is defined by the other without having to do any math.

    • This is misleading because while you can use substitution, it's more accurate that both equations represent the same line.

Correct statements:

  • 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.