In this lesson, you will examine solutions to different types of functions and determine if they are possible solutions by checking them algebraically. 

Graphing and checking the equations algebraically are ways to determine if the solutions to the systems of equations are possible. Let’s determine if the solutions for the systems of equations below are possible by checking algebraically.

1. Examine the following system of equations:

   x + y = 7

   2x - y = 2

   To determine if (3,4) is a valid solution, substitute 3 in for x and 4 in for y in both equations.  It must make both equations true to be a valid solution.

   Does (3) + (4) = 7 ?
   Does 2(3) - (4) = 2 ?

   Interactive popup. Assistance may be required.

   Check Your Answer

   Yes!
   If (3,4) satisfies both equations, does this imply it is the only solution?
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   Check Your Answer

   No. There are several other systems that could cause more than one solution to occur. In the previous example, however, (3,4) happens to be the only solution.
2. In this final example, (2,5) is a solution to the system listed below.  For your final challenge, find another solution (x, y) that satisfies this system.      Hint: x > 6 and y < 6.

   y = x² + 1

   y = 2x + 1

   Interactive popup. Assistance may be required.

   Check Your Answer

   By plugging in and evaluating you should find that (0,1) is another point.

   1 = (0)² + 1

   1 = 2(0) + 1