Final answer:
To solve the system of equations, we can use the method of substitution. The solution to the system of equations is x = 0 and y = 6.
Step-by-step explanation:
To solve the system of equations 2x + 3y = 18 and 3x + y = 6, we can use the method of substitution. First, solve one of the equations for one variable, for example, solve the second equation for y:
y = 6 - 3x
Then, substitute this value of y into the first equation:
2x + 3(6 - 3x) = 18
Simplify and solve for x:
2x + 18 - 9x = 18
-7x = 0
x = 0
Substitute this value of x back into either equation to find y:
y = 6 - 3(0) = 6
Therefore, the solution to the system of equations is x = 0 and y = 6.