Question 814665
x+6y=11
2x-3y=7

Multiply the top equation by -2
-2x -12y = -22
2x  -3y =  7
Adding the above together
    -15y = -15
Divide each side by -15
      y = 1
Substituting into x+6y=11
      x+6(1)=11
      x + 6 = 11
      x = 5
      x = 5
Verifying in each equation
x+6y=11  5 + 6(1) = 11 , 5 + 6 = 11 , so this checks.
2x-3y=7  2(5) -3(1) = 10 -3 = 7 , so this checks.