Determine if the following system of equations has no solutions, infinitely many solutions or
exactly one solution.

Ask by Ortiz Bob. in the United States

Dec 20,2024

Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $$ \begin{aligned} 5 x+y=-3 \ -5 x-y=3\end{aligned} $$

UpStudy AI · Accepted Answer

To determine the number of solutions for the system of equations:

$$
\begin{aligned}
5x + y &= -3 \quad \text{(1)} \
-5x - y &= 3 \quad \text{(2)}
\end{aligned}
$$

**Step 1: Analyze the Equations**

Let's examine if one equation is a multiple of the other.

Multiply equation (1) by $$-1$$:

$$
-1 \times (5x + y) = -1 \times (-3) \
-5x - y = 3 \quad \text{(which is exactly equation (2))}
$$

**Step 2: Conclusion**

Since equation (2) is just $$-1$$ times equation (1), both equations represent the same line. This means there are infinitely many solutions where both equations overlap.

**Final Answer:**

The system has infinitely many solutions.
The system has infinitely many solutions.

Determine if the following system of equations has no solutions, infinitely many solutions or
exactly one solution.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions