7. $$ \left\{\begin{array}{l}y=2 x+1 \ 2 x-y=3\end{array} ight. $$

Question

7. $$ \left\{\begin{array}{l}y=2 x+1 \ 2 x-y=3\end{array}ight. $$

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
y = 2x + 1 \quad \text{(1)} \
2x - y = 3 \quad \text{(2)}
\end{cases}
$$

**Step 1: Substitute Equation (1) into Equation (2)**

Since Equation (1) gives $$ y $$ in terms of $$ x $$, we can substitute $$ y = 2x + 1 $$ into Equation (2):

$$
2x - (2x + 1) = 3
$$

**Step 2: Simplify the Equation**

$$
2x - 2x - 1 = 3
$$
$$
-1 = 3
$$

**Step 3: Analyze the Result**

The equation $$ -1 = 3 $$ is a **contradiction**, which means there's no possible value of $$ x $$ that satisfies both equations simultaneously.

**Conclusion:**

The system of equations has **no solution**. Geometrically, this means that the two lines are **parallel** and do not intersect.

$$
\boxed{\text{No solution}}
$$
The system of equations has no solution.

7. \( \left\{\begin{array}{l}y=2 x+1 \\ 2 x-y=3\end{array}\right. \)