Question

1. \

$$\begin{cases} 2x + y = -10 \\\\ -y = 2x + 10 \\end{cases}$$

Explanation:

Step1: Identify the system of equations

We have the system:

$$
LATEXBLOCK0
$$

Let's rewrite the second equation to be in the same form as the first. Add \(y\) to both sides and subtract \(2x + 10\) from both sides of the second equation:
\( -2x - 10 = y \), which is the same as \(y = -2x - 10\)
The first equation is \(y = -2x - 10\) (by subtracting \(2x\) from both sides: \(y = -2x - 10\))

Step2: Analyze the system

Both equations simplify to \(y = -2x - 10\). This means the two equations are actually the same line (they are dependent and consistent). So, there are infinitely many solutions, and the solution set is all ordered pairs \((x, y)\) such that \(y = -2x - 10\) (or equivalently, \(2x + y = -10\)).

Answer:

The system of equations has infinitely many solutions, and the solution is all ordered pairs \((x, y)\) satisfying \(2x + y = -10\) (or \(y = -2x - 10\)).