Question

Find all solutions of the given system of equations and check your answer graphically. HINT [See Examples 2–5.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).)
x − y = 0
x + y = 8
(x, y) =

Answer 1

The values of (x,y)=(4,4). In terms of x, the value y(x)=8-x, If the given equation is $x-y=0$ and $x+y=8$.

Step-by-step explanation:

The given is,

                              $x-y=0$...............................(1)

                              $x+y=8$...............................(2)

Step:1

          Solution can be obtained by Elimination method,

          Equation (1) is multiplied by (-1)           ( Eqn (1) × -1 )

                             $-x+y=0$..............................(3)

          Substrate the equation (1) and equation (3),

                              $-x+y=0$

                                $x+y=8$

         ( - )

         $(-x-x)+(y-y)=(0-8)$

                             $(-2x)=-8$

                                $-2x = -8$

         we can cancel the minus because it is available in both sides,

                                  $2x=8$

                                    $x = \frac{8}{2}$

                                     x = 4

        From the value of x, Equation (2) becomes,

                              $x+y=8$

                               $4+y=8$

                                     $y = 8-x$    (Value of y in terms of x)

        Where, x = 4

                                     $y = 8-4$        

                                     $y =4$

Step:2

       Check for solution,

                             $x+y=8$.....................................(2)

       Substitute the values of x and y,

                             4 + 4 = 8

                                   8 = 8

Result:

         The values of (x,y)=(4,4). In terms of x, the value y(x)=8-x, where x=4. If the given equation is $x-y=0$ and $x+y=8$.