Question

Complete the statement with an equation that makes the statement true.(1 point)
The system of equations 3x+4y=1
and y=
has an infinite number of solutions.

Answer 1

For the system of equations to have an infinite number of solutions, the second equation must be equivalent to the first one when rearranged.

The first equation is given as:

\[ 3x + 4y = 1. \]

To express \( y \) in terms of \( x \), we can solve for \( y \):

1. Subtract \( 3x \) from both sides:

\[ 4y = 1 - 3x. \]

2. Divide by 4:

\[ y = \frac{1 - 3x}{4}. \]

Now any multiple or transformation of this equation can also represent the same line. For instance, if we multiply the entire equation by \( 2 \), we get:

\[ y = \frac{2(1 - 3x)}{4} = \frac{1 - 3x}{2}. \]

Thus, a valid equation for \( y \) that would give the system infinite solutions is:

\[ y = \frac{1 - 3x}{4}. \]

To ensure it's clear:

**Answer:** \( y = \frac{1 - 3x}{4} \) (or any equivalent form such as \( y = \frac{1 - 3x}{2} \)).