SOLUTION: y=-x+7 and y=x+1

They want you solve this system of two equations in two unknowns

    y = -x + 7

    y =  x + 1.


Add these equations (side by side).  You will get

    2y = 7 + 1

    2y = 8

     y = 8/2 = 4.


Now substitute this found value y= 4 into the second given equation.  You will get

    4 = x + 1.


It implies  

    4 - 1 = x.

    x = 3.


ANSWER.  The solution to the given problem is  x= 3,  y= 4.


You may check that the solution is correct by substituting the values into the original equations.