Question 72244
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graph each system of equations. then determine whether the system of equations has one solution, no solution, or infinitely many solutions. if the system has one solution name it.
x-y=9
x+y=11


To solve systems of linear equation, we can use substitution method, graphing or elimination method.

Let us use Elimination method
     x - y = 9     Eliminate y and solve for x
     x + y = 11
    ____________
    2x     = 20
         x = 10

Substitute x = 10 to any of the two equations

     x + y = 11
     10 + y = 11
         y = 11 - 10
         y = 1

Checking
     x - y = 9
    10 - 1 = 9
         9 = 9   ----------->True

     x + y = 11
    10 + 1 = 11
        11 = 11  ----------->True

Therefore the system has one solution ( 10, 1)

{{{graph (200, 200, -4, 14, -5, 15, -x+11, x-9)}}}

Notice that the two lines intersect when x = 10 and y = 1

so the solution means intersection of the two equations