-x - 4y = 2

Question

x + 4y = -2

Choose one of the following

The system has no solution
The system had a unique solution:
(x,y) = (___ ____)
Thr system had infinitely many solutions

Answer 1

To solve the system of equations:

1. \(-x - 4y = 2\)
2. \(x + 4y = -2\)

We can first rewrite the first equation and align it with the second equation:

\(-x - 4y = 2\) can be rewritten as \(x + 4y = -2\).

Notice that both equations can be simplified to the same single equation:

\[ x + 4y = -2 \]

Since both equations are the same, this means there are infinitely many solutions that satisfy this equation.

Thus, the answer is:

The system had infinitely many solutions.