What are the coordinates of the point on the line $5x-9y=42$ such that the $x$ and $y$ coordinates are the additive inverses of each other? Express your answer as an ordered pair.
I know that additive inverses are numbers that add up to zero, like 3 and -3. So I want to find a point $(x,y)$ on the line $5x-9y=42$ such that $x+y=0$. I can use this equation to eliminate one of the variables and solve for the other. If I substitute $y=-x$ into the equation of the line, I get $5x-9(-x)=42$. Simplifying, I get $14x=42$, so $x=3$. Then, since $y=-x$, I get $y=-3$. Therefore, the point I'm looking for is $(3,-3)$.

