Solve the system of equations: { y = -2x - 1, { 6y = 5 - x.

Solution:

Let's solve this system of equations step by step.

1. Step 1: Substitute the value of y from the first equation into the second equation.

   We have y = -2x - 1. Substituting this into 6y = 5 - x, we get:

   6(-2x - 1) = 5 - x

2. Step 2: Simplify and solve for x.

   Expanding the equation:

   -12x - 6 = 5 - x

   Add 12x to both sides:

   -6 = 5 + 11x

   Subtract 5 from both sides:

   -11 = 11x

   Divide by 11:

   x = -1

3. Step 3: Substitute the value of x back into the first equation to find y.

   y = -2x - 1

   y = -2(-1) - 1

   y = 2 - 1

   y = 1

Answer: x = -1, y = 1