Question

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

no solution
no solution

infinite solutions
infinite solutions

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

(−1,2)

Answer 1

To solve the system of equations using the substitution method, we'll start with the two equations:

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

First, let's simplify Equation 2. Notice we can factor out -2:

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

This shows that Equation 2 is actually just a multiple of Equation 1. Therefore, the two equations describe the same line.

Next, we can conclude that:

- Since they are the same line, there are infinite solutions to the system.

Thus, the answer is: **infinite solutions**.