jmc

Question

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.

Accepted Answer

Our point lies on 5x-9y=42 with the condition that x=-y. Thus, we have the system of equations align* 5x-9y &= 42 x &= -y. align* Substituting x= -y into the first equation gives align* 5(-y) -9y &=42 -14y &= 42 y &=-3. align* Thus x = -y = -(-3) = 3, so our desired point is (3,-3).