x-y=3 and xy-5x+y=-13

x-y=3 and xy-5x+y=-13

Using the first equation we can rearrange it as y = x -3    and substituting this in the second, we have

x(x -3) - 5x + (x -3) = -13   simplify

x ^2  - 3x - 5x + x -3 = -13

x^2 - 7x + 10  = 0      factor

(x -5) ( x-2) = 0   and setting each factor to 0, we have that x = 5 and x =2

And using y = x -3, when x = 5, y = 2   and when x = 2 , y = -1

So...our solutions (intersection points) are (5,2) and (2, -1)

Here's the graph of both equations.....https://www.desmos.com/calculator/3gd27vhg4y

The first graph is a line and the second is a "rotated" conic (in this case, a hyperbola)