Answer
$(\frac{13}{7},\frac{2}{7})$
Work Step by Step
The given pair of linear equations are.
$6x-4y=10$ ..... (1)
$2x+y=4$ ...... (2)
Multiply equation (2) by $4$.
$8x+4y=16$ ..... (3)
Add equation (1) and (3).
$\Rightarrow 6x-4y+8x+4y=10+16$
Simplify.
$\Rightarrow 14x=26$
Divide both sides by $14$.
$\Rightarrow x=\frac{26}{14}$
Simplify.
$\Rightarrow x=\frac{13}{7}$
Substitute the value of $x$ into equation (2).
$\Rightarrow 2(\frac{13}{7})+y=4$
Simplify.
$\Rightarrow \frac{26}{7}+y=4$
Isolate $y$.
$\Rightarrow y=4-\frac{26}{7}$
Simplify.
$\Rightarrow y=\frac{28}{7}-\frac{26}{7}$
$\Rightarrow y=\frac{28-26}{7}$
$\Rightarrow y=\frac{2}{7}$
Hence, the ordered pair of the point of intersection is $(x,y)=(\frac{13}{7},\frac{2}{7})$.
