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Alchen [17]
3 years ago
12

Solve the following system of equations and select the correct answer below:

Mathematics
1 answer:
Sauron [17]3 years ago
5 0
3x + 3y + 2z = -5 ⇒ 3x + 3y + 2z = -5 ⇒ 3x + 3y + 2z =   -5
1x + 1y + 3z = -4 ⇒ 1x + 1y + 3z = -4 ⇒ 3x + 3y + 9z = -12
3x -  1y + 5z = -8                                                    -7z = 7
                                                                                -7    -7
                                                                                  z = -1
3x + 3y + 2z = -5                                                      
1x + 1y + 3z = -4 ⇒ 1x + 1y + 3z = -4
3x -  1y + 5z = -8 ⇒ 3x -  1y + 5z = -8
                                        4x + 8z = -12     

     4x + 8z = -12
 4x + 8(-1) = -12
       4x - 8 = -12
           + 8    + 8
            4x = -4
             4      4
              x = -1

        3x + 3y + 2z = -5
3(-1) + 3y + 2(-1) = -5
           -3 + 3y - 2 = -5
             3y - 3 - 2 = -5
                  3y - 5 = -5
                      + 5  + 5
                       3y = 0
                        3     3
               (x, y, z) = (-1, 0, -1)
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Remember that <span>an extraneous solution of an equation, is the solution that emerges from solving the equation but is not a valid solution.
 
Lets solve our equation to find out what is the extraneous solution:
</span>\sqrt{x-3} =x-5
(\sqrt{x-3})^2 =(x-5)^2
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So, the solutions of our equation are </span>x=4 and x=7. Lets replace each solution in our original equation to check if they are valid solutions:
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- For x=4
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