Question

1. $x + y = -2$

$-3x - 3y = 6$

Explanation:

Step1: Simplify the second equation

Notice that the second equation \(-3x - 3y = 6\) can be simplified by dividing both sides by \(-3\). So we have \(\frac{-3x - 3y}{-3}=\frac{6}{-3}\), which simplifies to \(x + y=-2\).

Step2: Analyze the two equations

The first equation is \(x + y=-2\) and the second equation, after simplification, is also \(x + y=-2\). This means that the two equations represent the same line.

Step3: Determine the solution set

When two equations represent the same line, there are infinitely many solutions because every point on the line satisfies both equations. The solution can be expressed as all ordered pairs \((x,y)\) such that \(x + y=-2\), or we can solve for one variable in terms of the other, for example, \(y=-x - 2\), where \(x\) can be any real number.

Answer:

There are infinitely many solutions, which can be expressed as \((x,y)\) where \(x + y=-2\) (or \(y=-x - 2\) for any real number \(x\)).