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Use the substitution method to solve the system 2x+3y=4

, −4x−6y=−8
.(1 point)
Responses

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

no solution
no solution

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

infinite solutions

1 answer

To solve the system of equations using the substitution method, let’s first analyze the given equations:

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

Next, notice that Equation 2 can be simplified. By dividing the entire equation by -2, we get:

\[ 2x + 3y = 4 \]

Thus, we see that both equations represent the same line. Therefore, they are dependent, meaning there are infinite solutions.

Hence, the correct answer is:

infinite solutions