Answer
$(\frac{40}{9},\frac{5}{3})$.
Work Step by Step
The given pair of linear equations are.
$3x-2y=10$ ..... (1)
$3x+4y=20$ ...... (2)
Multiply equation (1) by $2$.
$6x-4y=20$ ..... (3)
Add equation (2) and (3).
$\Rightarrow 3x+4y+6x-4y=20+20$
Simplify.
$\Rightarrow 9x=40$
Divide both sides by $9$.
$\Rightarrow x=\frac{40}{9}$
Substitute the value of $x$ into equation (2).
$\Rightarrow 3(\frac{40}{9})+4y=20$
Simplify.
$\Rightarrow \frac{40}{3}+4y=20$
Divide both sides by $4$.
$\Rightarrow \frac{10}{3}+y=5$
Isolate $y$.
$\Rightarrow y=5-\frac{10}{3}$
Simplify.
$\Rightarrow y=\frac{15}{3}-\frac{10}{3}$
$\Rightarrow y=\frac{15-10}{3}$
$\Rightarrow y=\frac{5}{3}$
Hence, the ordered pair of the point of intersection is $(x,y)=(\frac{40}{9},\frac{5}{3})$.
