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CHOOSE 2 ANSWERS. Select the statement(s) that correctly describes the solution to this system of equations:

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 2 ANSWERS

1 answer

To analyze the system of equations:

  1. First equation: \(8x - 2y = -4\)
  2. Second equation: \(4x - y = -2\)

Let's simplify both equations to determine their nature.

First Equation: Divide the entire equation by 2: \[ 4x - y = -2 \]

Second Equation: The second equation remains: \[ 4x - y = -2 \]

Now we can see that both equations are identical: \[ 4x - y = -2 \]

Since they represent the same line, there are infinitely many solutions that satisfy both equations.

Correct Statements:

  • 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.

Thus, the two correct answers are:

  • 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.

(Note: It's crucial to recognize that the mention of parallel lines is typically incorrect given that these lines are actually the same; hence the statement about parallel lines with no solutions is misleading. The correct choices based on the properties of the given equations are the first option about infinite solutions.)