To solve by substitution, the first thing to do is solve for one of the variables. In this case, it is easiest to solve for x. To solve for x, add 4y to both sides of the equation.
x-4y = 9 , so x = 4y+9
Next, plug the x value, x = 4y+9, into the other equation, 2x-3y=11, and solve for y.
2(4y+9)-3y =11, so 8y+18-3y =11, and therefore 5y+18=11. Subtract 18 from both sides to get 5y = -7 and divide both sides by 5 to find y = -7/5.
Now, plug the y value into the equation that we found earlier for x. x = 4y+9, y = -7/5.
x = 4(-7/5) +9
x = -28/5 + 9
The common denominator of these numbers is 5, so change 9 to 45/5.
x = -28/5 + 45/5, and therefore x = 17/5
x = 17/5 and y = -7