To determine how many solutions exist for the system of equations:
1. First equation:
2x + 6y = 5
2. Second equation:
x + 3y = 2
we can use substitution or elimination methods to analyze it.
Step 1: Solve the second equation for x
Rearranging the second equation gives us:
x = 2 - 3y
Step 2: Substitute into the first equation
We can substitute the expression for x into the first equation:
2(2 - 3y) + 6y = 5
Expanding this results in:
4 - 6y + 6y = 5
This simplifies down to:
4 = 5
Since this statement is not true, it indicates that there is no solution to this system of equations.
Conclusion
Thus, the system of equations has no solutions.