### Instruction: What is the intersection of the lines given by $2y=-x+3$ and $-y=5x+1$?  Enter the answer as an ordered pair.### Response: Let's start by solving the second equation for y.
y = -5x - 1.
Now we can substitute that into the first equation.
2(-5x - 1) = -x + 3.
Simplifying gives -10x - 2 = -x + 3.
Adding x to both sides gives -9x - 2 = 3.
Adding 2 to both sides gives -9x = 5.
Finally, dividing both sides by -9 gives x = -5/9.
Now we can substitute that back into the equation y = -5x - 1.
y = -5(-5/9) - 1.
Simplifying gives y = 25/9 - 1.
y = 25/9 - 9/9.
So y = 16/9.