Line a: y = 2x + 3
line b: y = -x

where will these two lines intersect?

There are different ways to solve this:

Substitution:

in the equation: y = 2x + 3 every time you see a y insert -x in its place. This will solve for the x of the intersect

-x = 2x + 3

(-x-2x) = (2x - 2x) + 3

x = - 1

to solve for y incert x which is -1 into the equation y = 2x + 3

y = 2(-1) + 3

y = -2 + 3

y = 1

(-1,1)

 Hope this helped! Let me know if you want the other methods of solving this explained as well!