Tell whether the system has one solution, infinitely many solutions, or no solution.
1.5x+2y=11 3x+6y=22
To determine whether the system has one solution, infinitely many solutions, or no solution, we can use the method of elimination or substitution. In this case, let's use the method of elimination.
We can multiply the first equation by 2 to make the coefficients of y the same in both equations:
2(1.5x + 2y) = 2(11)
Simplifying, we get:
3x + 4y = 22
Now we have the following system of equations:
3x + 4y = 22
3x + 6y = 22
By subtracting the first equation from the second equation, we can eliminate x:
(3x + 6y) - (3x + 4y) = 22 - 22
2y = 0
y = 0
Now we can substitute the value of y back into one of the original equations to solve for x:
1.5x + 2(0) = 11
1.5x = 11
x = 11/1.5
x = 7.33
Therefore, the system has one solution, with x = 7.33 and y = 0.