Answer
$\{\left (\frac{11}{19},\frac{7}{19} \right )\}$.
Work Step by Step
The given system of equations are
$\Rightarrow 2x+5y=3$......(1)
$\Rightarrow 3x-2y=1$......(2)
Multiply equation (1) by 2 and equation (2) by 5 and then add.
$\Rightarrow 2(2x+5y)+5(3x-2y)=2(3)+5(1)$
Simplify.
$\Rightarrow 4x+10y+15x-10y=6+5$
Add like terms.
$\Rightarrow 19x=11$
Divide both sides by $19$.
$\Rightarrow \frac{19x}{19}=\frac{11}{19}$
Simplify.
$\Rightarrow x=\frac{11}{19}$
Substitute the value of $x$ into equation (1).
$\Rightarrow 2(\frac{11}{19})+5y=3$
Simplify.
$\Rightarrow \frac{22}{19}+5y=3$
Multiply the equation by $19$
$\Rightarrow 19\cdot \left ( \frac{22}{19}+5y \right )=19\cdot (3)$
Apply distributive property.
$\Rightarrow 22+95y=57$
Subtract $22$ from both sides.
$\Rightarrow 22+95y-22=57-22$
Add like terms.
$\Rightarrow 95y=35$
Divide both sides by $95$
$\Rightarrow \frac{95y}{95}=\frac{35}{95}$
Simplify.
$\Rightarrow y=\frac{7}{19}$
The solution set is $\{\left (x,y \right )\}=\{\left (\frac{11}{19},\frac{7}{19} \right )\}$.
