SOLUTION: 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.

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)







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



so the solution means intersection of the two equations