Answer
$\left(\dfrac{11}{19},\dfrac{7}{19}\right)$
Work Step by Step
We are given the system:
$\begin{cases}
2x+5y=3\\
3x-2y=1
\end{cases}$
We will use the addition method. Multiply Equation 1 by 3, Equation 2 by -2 and add them to eliminate $x$ and determine $y$:
$\begin{cases}
3(2x+5y)=3(3)\\
-2(3x-2y)=-2(1)
\end{cases}$
$3(2x+5y)-2(3x-2y)=3(3)-2(1)$
$6x+15y-6x+4y=7$
$19y=7$
$y=\dfrac{7}{19}$
Substitute the value of $y$ in Equation 1 to determine $x$:
$2x+5y=3$
$2x+5\left(\dfrac{7}{19}\right)=3$
$2x+\dfrac{35}{19}=3$
$2x=3-\dfrac{35}{19}$
$2x=\dfrac{22}{19}$
$x=\dfrac{11}{19}$
The system's solution is:
$\left(\dfrac{11}{19},\dfrac{7}{19}\right)$
