Solve the system of equations.
13x−y=90
y=x^2−x−42

Solve the first for y

y=13x-90 and the second is y=x^2-x-42

When there is/are solutions y=y so we can say:

x^2-x-42=13x-90  subtract 13x from both sides

x^2-14x-42=-90  add 90 to both sides

x^2-14x+48=0  expand so that it is easy to factor...

x^2-6x-8x+48=0 now factor 1st and 2nd pair of terms

x(x-6)-8(x-6)=0

(x-8)(x-6)=0

So there are two solutions, when x=6 and 8.

Using either original equation we can find the corresponding values for y.  I'll use y=13x-90 because it is easier...

y(6)=-12, y(8)=14  so the two solutions are the points:

(6,-12) and (8,14)