Answer
$(1,-2)$
Work Step by Step
Multiplying the first equation by $3$ and multiplying the second equation by $4$, the given system
\begin{align*}\require{cancel}
2x-4y&=10
\\
9x+3y&=3
\end{align*}is equivalent to
\begin{align*}\require{cancel}
6x-12y&=30
\\
36x+12y&=12
.\end{align*}
Adding the two equations above results to
\begin{align*}\require{cancel}
42x&=42
\\\\
\dfrac{\cancel{42}x}{\cancel{42}}&=\dfrac{42}{42}
\\\\
x&=1
.\end{align*}
Substituting $x=1$ into the first equation, $(2x-4y=10)$, results to
\begin{align*}\require{cancel}
2(1)-4y&=10
\\
2-4y&=10
\\
-4y&=10-2
\\
-4y&=8
\\\\
\dfrac{\cancel{-4}y}{\cancel{-4}}&=\dfrac{8}{-4}
\\\\
y&=-2
.\end{align*}
Hence, the solution of the given system is $(x,y)=(1,-2)$.
