Solve the Linear Equation Pair: 6x + y = 12 and 3y + 2x = 20

To solve this system of linear equations using the elimination method, follow these steps:

• Step 1: Align the equations for elimination. These equations are already simple, but you could multiply the first equation by 3 to align coefficients for $y$.
• Step 2: Multiply the first equation by 3 to facilitate elimination of $y$:
  $3(6x + y) = 3 \times 12$
  Thus, we get:
  $18x + 3y = 36$.
• Step 3: Rewrite and subtract the second equation from this new equation:
  $18x + 3y - (3y + 2x) = 36 - 20$,
  This simplifies to:
  $16x = 16$.
• Step 4: Solve for $x$:
  $x = \frac{16}{16} = 1$.
• Step 5: Substitute $x = 1$ back into the first original equation to find $y$:
  $6(1) + y = 12$,
  $6 + y = 12$,
  $y = 12 - 6$,
  $y = 6$.

Therefore, the solution to the system of equations is $x = 1, y = 6$.