\begin{tabular}{|l|}\hline 4 Listen \end{tabular} What is the solution to the system of equations? $$ \left\{\begin{array}{l}4 x-\frac{1}{2} y=11 \ -4 x+3 y=15\end{array} ight. $$ infinitely many solutions $$ (0,-22) $$ no solution $$ \left(\frac{4}{2},-2 ight) $$

Question

\begin{tabular}{|l|}\hline 4 Listen \end{tabular} What is the solution to the system of equations? $$ \left\{\begin{array}{l}4 x-\frac{1}{2} y=11 \ -4 x+3 y=15\end{array}ight. $$ infinitely many solutions $$ (0,-22) $$ no solution $$ \left(\frac{4}{2},-2ight) $$

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
4x - \frac{1}{2}y = 11 \quad \text{(1)} \
-4x + 3y = 15 \quad \text{(2)}
\end{cases}
$$

**Step 1: Add the Two Equations**

Adding equations (1) and (2) to eliminate $$ x $$:

$$
4x - \frac{1}{2}y - 4x + 3y = 11 + 15
$$

$$
\left(4x - 4x\right) + \left(-\frac{1}{2}y + 3y\right) = 26
$$

$$
2.5y = 26 \quad \Rightarrow \quad y = \frac{26}{2.5} = \frac{52}{5} = 10.4
$$

**Step 2: Substitute $$ y $$ Back into One of the Equations**

Using equation (1):

$$
4x - \frac{1}{2} \times \frac{52}{5} = 11
$$

$$
4x - \frac{26}{5} = 11
$$

$$
4x = 11 + \frac{26}{5} = \frac{55}{5} + \frac{26}{5} = \frac{81}{5}
$$

$$
x = \frac{81}{20} = 4.05
$$

**Solution:**

$$
x = \frac{81}{20} \quad \text{and} \quad y = \frac{52}{5}
$$

$$
\left( \frac{81}{20}, \frac{52}{5} \right)
$$

**Conclusion:**

The system has a **unique solution**: $$\left( \frac{81}{20}, \frac{52}{5} \right)$$.

None of the provided options match this solution.
The system has a unique solution: $$ \left( \frac{81}{20}, \frac{52}{5} \right) $$.

4 Listen

What is the solution to the system of equations?

infinitely many solutions

no solution

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

4 Listen What is the solution to the system of equations? infinitely many solutions no solution