3. $$ \begin{aligned} x & =2 y+7 \ x & =y+4\end{aligned} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{aligned}
x &= 2y + 7 \quad \text{(1)} \
x &= y + 4 \quad \text{(2)}
\end{aligned}
$$

**Step 1: Set the equations equal to each other**

Since both equations are equal to $$ x $$, we can set the right-hand sides equal to each other:

$$
2y + 7 = y + 4
$$

**Step 2: Solve for $$ y $$**

Subtract $$ y $$ from both sides:

$$
2y - y + 7 = 4 \
y + 7 = 4
$$

Subtract 7 from both sides:

$$
y = 4 - 7 \
y = -3
$$

**Step 3: Substitute $$ y $$ back into one of the original equations to find $$ x $$**

Using equation (2):

$$
x = y + 4 \
x = -3 + 4 \
x = 1
$$

**Solution:**

$$
x = 1, \quad y = -3
$$
$$ x = 1 $$ and $$ y = -3 $$.

3. \( \begin{aligned} x & =2 y+7 \\ x & =y+4\end{aligned} \)