Solve this system of cquations: $$ \left\{\begin{array}{l}3 x-2 y=-8 \ y=\frac{3}{2} x-2\end{array} ight. $$

Question

Solve this system of cquations: $$ \left\{\begin{array}{l}3 x-2 y=-8 \ y=\frac{3}{2} x-2\end{array}ight. $$

UpStudy AI · Accepted Answer

To solve the given system of equations:

$$
\begin{cases}
3x - 2y = -8 \
y = \dfrac{3}{2}x - 2
\end{cases}
$$

we can use the **substitution method**. Here's a step-by-step solution:

### Step 1: Substitute $$ y $$ from the Second Equation into the First

From the second equation:
$$
y = \dfrac{3}{2}x - 2
$$

Substitute this expression for $$ y $$ into the first equation:
$$
3x - 2\left(\dfrac{3}{2}x - 2\right) = -8
$$

### Step 2: Simplify the Equation

Expand the terms:
$$
3x - 2 \times \dfrac{3}{2}x + 2 \times 2 = -8
$$
$$
3x - 3x + 4 = -8
$$

### Step 3: Combine Like Terms

Combine the $$ x $$-terms:
$$
0x + 4 = -8
$$
$$
4 = -8
$$

### Step 4: Analyze the Result

The equation $$ 4 = -8 $$ is a **contradiction**; it is never true. This means that there is no value of $$ x $$ and $$ y $$ that simultaneously satisfies both equations.

### Conclusion

**The system of equations has no solution.** This is because the two equations represent parallel lines with the same slope but different y-intercepts, meaning they never intersect.

**Final Answer:**  
There is no solution to the system because the equations describe parallel lines.
There is no solution to the system because the equations represent parallel lines that never intersect.

Solve this system of cquations: \( \left\{\begin{array}{l}3 x-2 y=-8 \\ y=\frac{3}{2} x-2\end{array}\right. \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions