Question

1. $2x + 3y = -1$

$4x + 6y = 1$

Explanation:

Step1: Analyze the system of equations

We have the system:
\[

$$\begin{cases} 2x + 3y = -1 \\ 4x + 6y = 1 \end{cases}$$

\]
Notice that if we multiply the first equation by 2, we get \(4x + 6y=-2\). But the second equation is \(4x + 6y = 1\).

Step2: Check for consistency

For a system of linear equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\), if \(\frac{a_1}{a_2}=\frac{b_1}{b_2}
eq\frac{c_1}{c_2}\), the system is inconsistent (no solution).
Here, \(\frac{2}{4}=\frac{3}{6}=\frac{1}{2}\), but \(\frac{-1}{1}=-1
eq\frac{1}{2}\). So the system has no solution.

Answer:

The system of equations \(

$$\begin{cases}2x + 3y = -1 \\4x + 6y = 1\end{cases}$$

\) has no solution.