Final answer:
To solve the system of linear equations by substitution, isolate one variable and substitute it into the other equation. The solution to the given system is x = -3/4 and y = -9/2.
Step-by-step explanation:
To solve the system of linear equations by substitution, we need to isolate one variable in one equation and substitute it into the other equation. Let's solve the given system:
Equation 1: 8x + 13y = 0
Equation 2: 12x + 3 = y
First, we solve Equation 2 for y:
y = 12x + 3
Now, substitute this expression for y in Equation 1:
8x + 13(12x + 3) = 0
Simplify and solve for x:
8x + 156x + 39 = 0
164x + 39 = 0
164x = -39
x = -39/164 = -3/4
Now, substitute this value of x back into Equation 2 to find y:
y = 12(-3/4) + 3 = -9/2
Therefore, the solution to the system of linear equations is x = -3/4 and y = -9/2.