Question

at what point do the lines 5x +y=19 and-x +2y=6 intersect?

Answer 1

Set them both equal to y so that you can then set them equal to each other.
5x+y=19 ---------> y=19-5x
-x+2y= -6 --------->y= (x-6)/2

then substitute the y and set the equations equal to each other
19-5x= (x-6)/2
now solve for x
2(19-5x)=x-6
38-10x=x-6
44=11x
x=4


plug 4 in for x in either one of the original equations
5(4)+y=19
y= -1

so the answer is (4, -1)

Answer 2

thanks I understand now