12. $$ \left\{\begin{array}{l}4 x-y=-4 \ 5 x=2 y+1\end{array} ight. $$

Question

12. $$ \left\{\begin{array}{l}4 x-y=-4 \ 5 x=2 y+1\end{array}ight. $$

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
4x - y = -4 \quad \text{(1)} \
5x = 2y + 1 \quad \text{(2)}
\end{cases}
$$

**Step 1: Express $$ y $$ in terms of $$ x $$ from Equation (1).**

$$
4x - y = -4 \
\Rightarrow y = 4x + 4 \quad \text{(3)}
$$

**Step 2: Substitute Equation (3) into Equation (2).**

$$
5x = 2y + 1 \
5x = 2(4x + 4) + 1 \
5x = 8x + 8 + 1 \
5x = 8x + 9
$$

**Step 3: Solve for $$ x $$.**

$$
5x - 8x = 9 \
-3x = 9 \
x = -3
$$

**Step 4: Substitute $$ x = -3 $$ back into Equation (3) to find $$ y $$.**

$$
y = 4(-3) + 4 \
y = -12 + 4 \
y = -8
$$

**Solution:**
$$
x = -3, \quad y = -8
$$
The solution to the system of equations is $$ x = -3 $$ and $$ y = -8 $$.

12. \( \left\{\begin{array}{l}4 x-y=-4 \\ 5 x=2 y+1\end{array}\right. \)