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Use the substitution method to solve the system 2x+3y=4, −4x−6y=−8.(1 point)

Responses

(2−1)
left parenthesis 2 comma negative 1 right parenthesis

no solution
no solution

(−1,2)
left parenthesis negative 1 comma 2 right parenthesis

infinite solutions

1 answer

To solve the system using the substitution method, we start with the given equations:

  1. \( 2x + 3y = 4 \)
  2. \( -4x - 6y = -8 \)

First, we can simplify the second equation. Notice that the second equation is a multiple of the first equation:

\[ -4x - 6y = -8 \implies 2x + 3y = 4 \]

This is just the first equation multiplied by -2. This means both equations represent the same line in the coordinate plane.

Since both equations are equivalent, we have infinite solutions along the line represented by either equation. Therefore, we can conclude that:

Answer: infinite solutions.