2: Determine if the point $$ (3,4) $$ lies on both of the lines in the system of equations by substituting the ordered pair into both equations. $$ \left.\begin{array}{r}4 x-3 y=0 \ -4 x+3 y=0\end{array} ight] $$

Question

2: Determine if the point $$ (3,4) $$ lies on both of the lines in the system of equations by substituting the ordered pair into both equations. $$ \left.\begin{array}{r}4 x-3 y=0 \ -4 x+3 y=0\end{array}ight] $$

UpStudy AI · Accepted Answer

To determine if the point $$ (3, 4) $$ lies on both lines of the system, we'll substitute $$ x = 3 $$ and $$ y = 4 $$ into each equation and check if the equations hold true.

**Given System of Equations:**
$$
\begin{cases}
4x - 3y = 0 \
-4x + 3y = 0
\end{cases}
$$

### 1. Substitute into the first equation $$ 4x - 3y = 0 $$:

$$
4(3) - 3(4) = 12 - 12 = 0
$$

**Result:** $$ 0 = 0 $$ ✓ **True**

### 2. Substitute into the second equation $$ -4x + 3y = 0 $$:

$$
-4(3) + 3(4) = -12 + 12 = 0
$$

**Result:** $$ 0 = 0 $$ ✓ **True**

### **Conclusion:**
Since the point $$ (3, 4) $$ satisfies both equations in the system, it **lies on both lines**.
The point $$ (3, 4) $$ lies on both lines in the system.

2: Determine if the point \( (3,4) \) lies on both of the lines in the system of equations by substituting the ordered pair into both equations. \( \left.\begin{array}{r}4 x-3 y=0 \\ -4 x+3 y=0\end{array}\right] \)

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions