To find the solution to the system of linear equations given by Equation 1: \( y = 3x - 2 \) and Equation 2: \( y = -x - 6 \), we can solve the system by checking if the lines intersect at a single point, which would be the solution to this system of equations.
The point of intersection is given as (-1, -5).
Now, we can check if this point satisfies both equations:
- Substitute \( x = -1 \) into Equation 1:
\[ y = 3(-1) - 2 = -3 - 2 = -5 \]
This matches the point (-1, -5).
- Substitute \( x = -1 \) into Equation 2:
\[ y = -(-1) - 6 = 1 - 6 = -5 \]
This also matches the point (-1, -5).
Since both equations are satisfied at the point (-1, -5), this means the two lines intersect at this point.
Thus, the solution to this system of linear equations is:
(-1, -5)