Answer
The system of equations has infinitely many solutions .
Solution set: $\left\{\left(\dfrac{-2-5y}{3}, \dfrac{-6-15y}{9}\right)\right\}$
Work Step by Step
We need to solve the given system of equations:
$$3x+5y=-2 ~~~(1) \\ 9x+15y=-6 ~~~(2)$$
Multiply the first equation by $-3$ to obtain the equivalent equation:
$$-9x-15y=6 ~~~~(3)$$
Add equations (2) and (3) to eliminate $x$.
$$9x+15y-9x-15y=-6+6 \\ 0=0 $$
Both variables were eliminated and resulted in a true equation/statement.
This means that the system has infinitely many solutions.
Solve for $x$ in the first equation to obtain:
\begin{align*}
3x+5y&=-2\\
3x&=-5y-2\\
x&=\dfrac{-5y-2}{3}
\end{align*}
Thus, the solution set is $\left\{\left(\dfrac{-2-5y}{3}, \dfrac{-6-15y}{9}\right)\right\}$.
