### Instruction: 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.### Response: 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 $y=-3$.