3x + 2y = 12
x - y = 2

Q: 3x + 2y = 12 x - y = 2

The system of equations is: \[ \begin{cases} 3x + 2y = 12 \\ x - y = 2 \end{cases} \] To solve it, we can use the substitution or elimination method. Here, I'll use substitution: 1. From the second equation, solve for $x$: \[ x = y + 2 \] 2. Substitute $x = y + 2$ into the first equation: \[ 3(y + 2) + 2y = 12 \] 3. Simplify and solve for $y$: \[ 3y + 6 + 2y = 12 \\ 5y + 6 = 12 \\ 5y = 6 \\ y = \frac{6}{5} \] 4. Substitute $y = \frac{6}{5}$ back into $x = y + 2$: \[ x = \frac{6}{5} + 2 = \frac{6}{5} + \frac{10}{5} = \frac{16}{5} \] So, the solution is $x = \frac{16}{5}$ and $y = \frac{6}{5}$.

Question

Accepted Answer

The system of equations is:

$$
\begin{cases} 
3x + 2y = 12 \
x - y = 2 
\end{cases}
$$

To solve it, we can use the substitution or elimination method. Here, I'll use substitution:

1. From the second equation, solve for $x$:
   $$
   x = y + 2
   $$

2. Substitute $x = y + 2$ into the first equation:
   $$
   3(y + 2) + 2y = 12
   $$

3. Simplify and solve for $y$:
   $$
   3y + 6 + 2y = 12 \
   5y + 6 = 12 \
   5y = 6 \
   y = \frac{6}{5}
   $$

4. Substitute $y = \frac{6}{5}$ back into $x = y + 2$:
   $$
   x = \frac{6}{5} + 2 = \frac{6}{5} + \frac{10}{5} = \frac{16}{5}
   $$

So, the solution is $x = \frac{16}{5}$ and $y = \frac{6}{5}$.

3x + 2y = 12 x - y = 2

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