Answer
The system of equations has infinitely many solutions.
Solution Set: $\left\{\left(-5y+9, y\right)\right\}$
Work Step by Step
We write the system of equations as:
$$x+5y=9 \quad \quad\quad\quad(1)\\
2x+10y=18 \quad \quad\space \space(2)$$
Multiply Equation $(1)$ by $-2$ to obtain the equivalent equation:
$$-2x-10y=-18 \quad \quad(3)$$
Add Equations $(2)$ and $(3)$ to obtain: .
$$(-2x-10y)+(2x+10y)=18-18 \\
0=0 $$
Since both variables were eliminated and the resulting equation is true, then it follows that the system of equations has infinitely many solutions.
To write the solution with $y$ arbitrary, solve for $x$ in equation $(1)$ to obtain:
\begin{align*}
x+5y&=9\\
x&=-5y+9\end{align*}
Therefore, the solution set with $y$ arbitrary is $\left\{\left(-5y+9, y\right)\right\}$.
