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 of equations is x = -10 and y = 7/3.
Step-by-step explanation:
To solve the system of linear equations by substitution, we first solve one equation for one variable, and then substitute the expression for that variable into the other equation. Let's start by solving the first equation for x:
1/3x + y = -1
1/3x = -1 - y
x = -3 - 3y
Now we substitute this expression for x into the second equation and solve for y:
1/3(-3 - 3y) + 8y = 13
-1 - y + 8y = 13
7y - y = 13 + 1
6y = 14
y = 14/6
y = 7/3
Next, we substitute the value of y back into the expression for x:
x = -3 - 3(7/3)
x = -3 - 7
x = -10
Therefore, the solution to the system of linear equations is x = -10 and y = 7/3.