If 2x + 3y = 12 and 3x + 5y = 20, what is the value of x + y?

Sure, let's solve the system of equations step by step to find the value of $x + y$.

The given system of equations is:

1. $2x + 3y = 12$
2. $3x + 5y = 20$

Step 1: Eliminate one variable

We can use the method of elimination to eliminate one of the variables. Let's eliminate $x$.

First, we need to make the coefficients of $x$ in both equations the same. We can do this by multiplying the first equation by 3 and the second equation by 2:

$3(2x + 3y) = 3(12) \implies 6x + 9y = 36$ $2(3x + 5y) = 2(20) \implies 6x + 10y = 40$

Step 2: Subtract the equations

Now, subtract the first modified equation from the second modified equation to eliminate $x$:

$(6x + 10y) - (6x + 9y) = 40 - 36$ $6x + 10y - 6x - 9y = 4$ $y = 4$

Step 3: Substitute $y$ back into one of the original equations

Now that we have $y = 4$, we can substitute this value back into one of the original equations to find $x$. Let's use the first equation:

$2x + 3y = 12$ $2x + 3(4) = 12$ $2x + 12 = 12$ $2x = 0$ $x = 0$

Step 4: Find $x + y$

Now that we have $x = 0$ and $y = 4$, we can find $x + y$:

$x + y = 0 + 4 = 4$

So, the value of $x + y$ is $4$.