Question 4999
Solve for one value in the first equation and then substitute this value in the second equation. Then enter the answer to the orginal equation. 

            #1. y = 6 - x
          2x - 3y = 22
      2x - 3(6-x) = 22
     2x - 18 - 3x = 22
2x - 18 + 18 - 3x = 22 + 18
          2x - 3x = 40
              -1x = 40
           -1x/-1 = 40/- 1
                x = -40
                y = 6 - 40
                y = -34
Check: enter in the x and y values into the orginal equation:
-34 = 6 -40
-34 = -34

       #2. x + 2y = 5
           x + y  = 2: x - x + y = 2 - x; y = 2 - x (rewrite equation)
   (fill in the y = 2 - x into the first equation)
     x + 2(2 - x) = 5
       x + 4 - 2x = 5
   x + 4 - 4 - 2x = 5 - 4
           x - 2x = 1
               -x = 1 
                x = -1
            x + y = 2
           -1 + y = 2
       -1 + 1 + y = 2 + 1
                y = 3
Check:
-1 + 2(3) = 5
-1 + 6 = 5    
5 = 5
        #3. x + y = 31
            x - y = 17
                x = 31 - y
       31 - y - y = 17
     31 - 31 - 2y = 17 - 31
              -2y = -14
           -2y/-2 = -14/-2
                y = 7

            x + y = 31
            x + 7 = 31
        x + 7 - 7 = 31 - 7
                x = 24  
Check:
24 + 7 = 31
31 = 31

        #4. 7x + y = 10: y = -7x + 10 
            2y + 5x = 11
   2(-7x + 10) + 5x = 11
     -14x + 20 + 5x = 11
-14x + 20 - 20 + 5x = 11 - 20
          -14x + 5x = -9
                -9x = -9
             -9x/-9 = -9/-9
                  x = -1

             7x + y = 10 
          7(-1) + y = 10
             -7 + y = 1
          7 - 7 + y = 10 - 7
                  y = -3

Check:
2(-3) + 5(-1) = 11
-6 + -5 = 11
Check:
7(1) + -6 = 10