Use the substitution method to solve the system x−2y=3, 4x−8y=12

Question

.(1 point)
a) 0,3
b) 3,0
c) no solutions
d) infinite solutions

Answer 1

To solve the system of equations using the substitution method, let's first express one variable in terms of the other using the first equation.

The given equations are:

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

First, let's solve the first equation for \( x \):

\[ x = 2y + 3 \]

Now we can substitute this expression for \( x \) into the second equation:

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

Expanding this gives:

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

The \( 8y \) terms cancel out:

\[ 12 = 12 \]

This is an identity, which means that the second equation does not provide any new information about the solution. Essentially, this indicates that the two equations represent the same line, resulting in infinite solutions.

Thus, the correct answer is:

d) infinite solutions