Answer
See below
Work Step by Step
Given: $3x+7y=1\\4x+5y=23$
Multiply the second equation by $-4$:
$-12x-28y=-4$
Multiply the second equation by $-3$
$12x+15y=69$
Then we have $-13y=65\\
\rightarrow y=-5$
Substitute: $3x+7(-5)=1\\
\rightarrow 3x=36\\
\rightarrow x=12$