Question

-x + y = 3
-2x + 2y = 3

Answer 1

To solve the system of equations:

1. \(-x + y = 3\)
2. \(-2x + 2y = 3\)

We can start by simplifying the second equation. We can divide the entire equation by 2:

\[
-x + y = \frac{3}{2}
\]

Now we rewrite the equations:

1. \(-x + y = 3\) (Equation 1)
2. \(-x + y = \frac{3}{2}\) (Equation 2)

Next, we observe that both equations represent the same left-hand side (-x + y), so we can set the right-hand sides equal to each other:

\[
3 = \frac{3}{2}
\]

This is not true, indicating that the two equations describe parallel lines that will never intersect. Therefore, there is no solution to this system of equations.

In summary, the system is inconsistent, and there are no values of \(x\) and \(y\) that satisfy both equations simultaneously.