Question

#11
-x - y = 2
6x + 6y = -12

Explanation:

Step1: Solve the first equation for x or y

From \(-x - y = 2\), we can express \(x\) in terms of \(y\):
\(-x = 2 + y\)
\(x = -y - 2\)

Step2: Substitute x into the second equation

Substitute \(x = -y - 2\) into \(6x + 6y = -12\):
\(6(-y - 2) + 6y = -12\)

Step3: Simplify the equation

Expand and simplify:
\(-6y - 12 + 6y = -12\)
\(-12 = -12\)

This is an identity, meaning the two equations are dependent (represent the same line) and have infinitely many solutions. The solution can be expressed as \(x = -y - 2\) (or \(y = -x - 2\)) for any real number \(x\) (or \(y\)).

Answer:

The system has infinitely many solutions, expressed as \(x = -y - 2\) (or \(y = -x - 2\)) where \(x, y \in \mathbb{R}\).