Question

Use the substitution method to solve the system x−2y=3
, 4x−8y=12
.(1 point)
Responses

no solution
no solution

(3,0)
left parenthesis 3 comma 0 right parenthesis

(0,3)
left parenthesis 0 comma 3 right parenthesis

infinite solutions

Answer 1

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

1. \( x - 2y = 3 \)
2. \( 4x - 8y = 12 \)

First, we can solve the first equation for \( x \):

\[
x = 2y + 3
\]

Next, we will substitute this expression for \( x \) into the second equation:

\[
4(2y + 3) - 8y = 12
\]

Expanding the left side:

\[
8y + 12 - 8y = 12
\]

This simplifies to:

\[
12 = 12
\]

Since this statement is always true, it indicates that there are infinitely many solutions. Specifically, the two original equations are equivalent, meaning they represent the same line.

Therefore, the answer is:

**infinite solutions**.