Systems of Equations Math Example 3

Solution

1. 1
   Step 1: From the second equation, express $x$ in terms of $y$: $x = y + 1$.
2. 2
   Step 2: Substitute into the first equation: $2(y + 1) + 3y = 12$, so $2y + 2 + 3y = 12$.
3. 3
   Step 3: Combine like terms: $5y + 2 = 12$, so $5y = 10$ and $y = 2$.
4. 4
   Step 4: Back-substitute: $x = 2 + 1 = 3$. Check: $2(3) + 3(2) = 12$ ✓ and $3 - 2 = 1$ ✓