### 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: To find the intersection of two lines, I need to find the values of x and y that satisfy both equations simultaneously.
One way to do this is to use the substitution method.
I can solve for y in one equation and then plug it into the other equation to get a single equation in x.
I choose the second equation, since it is easier to solve for y. I get $y=-5x-1$ by dividing both sides by -1.
Now I substitute this expression for y into the first equation, and I get $2(-5x-1)=-x+3$.
I simplify this equation by distributing the 2 and then collecting like terms.
I get $-10x-2=-x+3$, which implies $-9x=5$ and then $x=-5/9$.
Now that I have x, I can plug it back into either equation to find y. I choose the second equation again, since it is simpler.
I get $y=-5(-5/9)-1=25/9-1=16/9$.
Therefore, the intersection of the two lines is the point $(-5/9,16/9)$.