How do you solve for y in the equations x + 3y = 6 and 2x + 7y = 10?

To solve for y in the system of equations given:

1. x + 3y = 6
2. 2x + 7y = 10

We can use either substitution or elimination method. Here, we will use the substitution method:

1. First, let’s solve the first equation for x:

   x = 6 - 3y
   

2. Now, substitute this expression for x into the second equation:

   2(6 - 3y) + 7y = 10
   

3. This simplifies to:

   12 - 6y + 7y = 10
   

4. Combine like terms:

   12 + y = 10
   

5. Now, isolate y:

   y = 10 - 12
   y = -2
   

6. Now that we have y, we can substitute back to find x:

   x = 6 - 3(-2) = 6 + 6 = 12
   

In conclusion, the solution to the system of equations is:

   x = 12
   y = -2

Thus, the values of x and y are:

• x = 12
• y = -2