What is the point of intersection of lines -2x+y-1 and x+y-5?

These are not equations of lines because there are no
equal signs in the equations.

Assuming the equations
are...

-2x + y = 1

x + y =
5

Set both equations to equal
y.

-2x + y = 1               y = 1 +
2x

x + y = 5                  y = 5 -
x

Since both equations equal y, then they equal each
other.

1 + 2x = 5 - x

Solve
for x.

1 + 3x = 5

3x =
4

x = 4/3

Now substitute 4/3
in for x in one of the equations and solve for y.

y = 5 -
x

y = 5 - 4/3

y =
11/3

You can check this by substituting 4/3 for x and 11/3
for y in the other equation.

y =  1 +
2x

11/3 = 1 + 2 * 4/3

11/3 = 1
+ 8/3

11/3 = 11/3    
check!

Point of Intersection:  (4/3 ,
11/3)

This question can also be solved
graphically.  Rewrite both equations in slope-intercept
form.

y = -1x + 5

y = 2x +
1

Graph both equations and find the point of
intersection.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-1,3,-1,5,1,1,1,1,1,300,200,func,-1x+5,null,0,0,,,black,1,none,func,2x+1,null,0,0,,,black,1,none"/>

Notice
that the point of intersection is (4/3, 11/3) or ( class="AM">`~~` 1.3, `~~`
3.7).