Question

3x - 2y = 6\
15x - 10y = -2

Explanation:

Step1: Analyze the system of equations

We have the system:

$$
LATEXBLOCK0
$$

Notice that the second equation can be simplified by dividing all terms by 5: \(3x - 2y = -\frac{2}{5}\)

Step2: Compare the two equations

Now we have:
First equation: \(3x - 2y = 6\)
Second equation (simplified): \(3x - 2y = -\frac{2}{5}\)

But \(6
eq-\frac{2}{5}\), and the left - hand sides of both equations are the same (\(3x - 2y\)) while the right - hand sides are different. This means that the system of linear equations has no solution.

Answer:

The system of equations \(

$$\begin{cases}3x - 2y = 6\\15x - 10y=-2\end{cases}$$

\) has no solution.