How many solutions does the following system have
17=11y+12x
12x+11y=14
To find the number of solutions for the system, we can solve the equations and see if they have a unique solution, infinitely many solutions, or no solution.
First, let's solve the system:
We can rearrange the first equation to solve for y:
11y = 17 - 12x
y = (17 - 12x)/11
Now we can substitute this expression for y into the second equation:
12x + 11((17 - 12x)/11) = 14
12x + 17 - 12x = 14
17 = 14
This is a contradiction since the left side of the equation is not equal to the right side. Therefore, the system has no solution.
Answer: The system has no solution.