SOLUTION: Find the value of a and b so that the solution set is (10,11) a = b =

You didn't give the system of equations, so I will make up two 
equations.  Suppose the system of equations were, say this:

ax + by = 53
ax - by = -13

Then we substitute x=10 and y=11 into those:

a(10) + b(11) = 53
a(10) - b(11) = -13

or

10a + 11b =  53
10a - 11b = -13

We add those two equations term by term and get

20a       =  40

          a = 2

Substitute in

  10a - 11b = -13
10(2) - 11b = -13
   20 - 11b = -13
       -11b = -33
          b = 3

So if a = 2 and b = 3, then the system

ax + by = 53
ax - by = -13

will become

2x + 3y = 53
2x - 3y = -13

Checking to see:

Adding the two equations term by term gives:

4x     = 40
     x = 10

Substitute into

   2x - 3y = -13
2(10) - 3y = -13      
   20 - 3y = -13
       -3y = -33
         y = 11

So a=2 and b=3 checks.

Edwin