SOLUTION: Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution". 5x - 2y = 6 x = 5 - y

Algebra ->  Linear-equations -> SOLUTION: Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution". 5x - 2y = 6 x = 5 - y      Log On


   



Question 561575: Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution".
5x - 2y = 6
x = 5 - y

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution".
5x - 2y = 6
      x = 5 - y

The second equation is already solved for x, so
we substitute (5 - y) for x in the first equation:

      5x - 2y = 6
5(5 - y) - 2y = 6
 25 - 5y - 2y = 6
      25 - 7y = 6
          -7y = -19
            y = %28-19%29%2F%28-7%29
            y = 19%2F7

Substitute 19%2F7 for y in

      x = 5 - y
      x = 5 - 19%2F7
      x = 5·7%2F7 - 19%2F7
      x = 35%2F7 - 19%2F7
      x = 16%2F7

Solution:   (x,y) = (16%2F7,19%2F7)

Edwin