Final answer:
The system of equations given, -x + 2y = 10 and -3x + 6y = 11, are inconsistent and have no solution because they represent parallel lines that do not intersect.
Step-by-step explanation:
The system of equations given are:
- -x + 2y = 10
- -3x + 6y = 11
We need to solve this system of equations. First, notice that the second equation is just a multiple of the first equation. If you multiply the first equation by 3, you get the second equation. Mathematically:
- Multiply the first equation by 3 to get: -3x + 6y = 30
- Now, compare this with the second equation: -3x + 6y = 11
We see that the two equations are inconsistent (they cannot both be true at the same time for the same values of x and y), which suggests that there is no solution to this system of equations. This means that the lines represented by these equations are parallel and never intersect.