To solve the system of linear equations represented by:
- Equation 1: x + 3y = 2
- Equation 2: x + 3y = 16
We begin by examining both equations simultaneously. Notice that both equations have the same left-hand side, x + 3y, which implies that they describe parallel lines.
1. From Equation 1, we have:
x + 3y = 2
2. From Equation 2, we have:
x + 3y = 16
Simplifying both equations yields:
- From Equation 1: x + 3y = 2
- From Equation 2: x + 3y = 16
Since both equations equate x + 3y to different values (2 and 16), there is no point (x, y) that can satisfy both equations at the same time. Thus, the lines are parallel and there is no solution to this system of linear equations.
In conclusion, the system of equations is inconsistent, resulting in:
No Solution