Answer
$(\frac{41}{8},-\frac{15}{2})$
Work Step by Step
The given pair of linear equations are.
$4x+5y=-17$ ..... (1)
$4x+y=13$ ...... (2)
Multiply equation (2) by $-1$.
$-4x-y=-13$ ..... (3)
Add equation (1) and (3).
$\Rightarrow 4x+5y-4x-y=-17-13$
Simplify.
$\Rightarrow 4y=-30$
Divide both sides by $4$.
$\Rightarrow y=-\frac{30}{4}$
Simplify.
$\Rightarrow y=-\frac{15}{2}$
Substitute the value of $x$ into equation (2).
$\Rightarrow 4x+(-\frac{15}{2})=13$
Simplify.
$\Rightarrow 4x-\frac{15}{2}=13$
Isolate $x$.
$\Rightarrow x=\frac{1}{4}(13+\frac{15}{2})$
Simplify.
$\Rightarrow x=\frac{1}{4}(\frac{26}{2}+\frac{15}{2})$
$\Rightarrow x=\frac{1}{4}(\frac{26+15}{2})$
$\Rightarrow x=\frac{1}{4}(\frac{41}{2})$
$\Rightarrow x=\frac{41}{8}$
Hence, the ordered pair of the point of intersection is $(x,y)=(\frac{41}{8},-\frac{15}{2})$.
