Solve this system of equations $$ \left\{\begin{array}{l}4 x+3 y=11 \ 3 x-3 y=\quad-18\end{array} ight. $$ One or more solutions: ONo solution O Infinite number of solutions

Question

Solve this system of equations $$ \left\{\begin{array}{l}4 x+3 y=11 \ 3 x-3 y=\quad-18\end{array}ight. $$ One or more solutions: ONo solution O Infinite number of solutions

UpStudy AI · Accepted Answer

**Step 1: Write down the system of equations**
$$
\begin{cases}
4x + 3y = 11 \
3x - 3y = -18
\end{cases}
$$

**Step 2: Add the two equations**

Adding the equations eliminates $$ y $$:
$$
(4x + 3y) + (3x - 3y) = 11 + (-18)
$$
$$
4x + 3x + 3y - 3y = -7
$$
$$
7x = -7
$$
$$
x = \frac{-7}{7} = -1
$$

**Step 3: Substitute $$ x = -1 $$ into one of the original equations**

Using the first equation:
$$
4(-1) + 3y = 11
$$
$$
-4 + 3y = 11
$$
$$
3y = 11 + 4
$$
$$
3y = 15
$$
$$
y = \frac{15}{3} = 5
$$

**Step 4: Write the solution**

The unique solution to the system is:
$$
(x, y) = (-1, 5)
$$

**Conclusion:** There is one unique solution.
There is one unique solution: $$ x = -1 $$ and $$ y = 5 $$.

Solve this system of equations

One or more solutions:
ONo solution
O Infinite number of solutions

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Solve this system of equations One or more solutions: ONo solution O Infinite number of solutions