Question 5000
to add you need to eliminate one of your variables
1)
 x-y=6
 +3x+y=-2
___________
   4x=4 divide bothe sides by 4
x=1

3(1)+y=-2
3+y=-2 subtract 3 from both sides
y=-5

2)
 3x-4y=7
  + x+4y=5
___________
    4x=12
x=3         
3+4y=5   
4y=2
y=.5

3)
4x+5y=5 = [3]4x+5y=5 = 12x+15y=15
+ 6x+7y=7 = [-2]6x+7y=7 =-12x-14y=-14
______________________________________
                         y=1
4x+5(1)=5 
4x=0
x=0

4)
2x+3y=13 = [5]2x+3y=13 = 10x+15y=65
+3x-5y=10 =[3]3x-5y=10 = 9x-15y=30
_____________________________________
                          x=95
3(95)-5y=10 = 285-5y=10
            -5y=-275
              y=55

5)
  x+y=4 = [-2]x+y=4 = -2x-2y=-8
+2x+3y=7 = 2x+3y=7 = + 2x+3y=7
_______________________________
                       y=-1
x+(-1)=4
x=5

6)
 8x-10y=2 =                   8x-10y=2
+7x-5y=13 = [-2]7x-5y=13 = + -14x+10y=-26
________________________________________
                  -6x=-24
                x=4
32-10y=2
-10y=-30
y=3