Final answer:
To solve the system of linear equations by substitution, solve one equation for one variable and substitute it into the other equation. The solution to the given system is x = 4 and y = 3/2.
Step-by-step explanation:
To solve the system of linear equations by substitution, we will solve one equation for one variable and substitute that expression into the other equation. Let's solve the second equation for x:
6y = x + 5
x = 6y - 5
Now substitute this expression for x in the first equation:
-5(6y - 5) + 6y = -11
-30y + 25 + 6y = -11
-24y = -36
y = -36 / -24
y = 3/2
Now substitute this value of y back into either of the original equations to find x:
6(3/2) = x + 5
9 = x + 5
x = 9 - 5
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 3/2.