Answer
The error is in step 2. See below for correction.
Solution: $(\displaystyle \frac{7}{51},\frac{133}{51})$
Work Step by Step
Step 1 is good because the second equation has been chosen to be solved for x.
Step 2 is faulty, because it does not represent the second equation with x substituted with $21-8y.$
$x$ has been substituted into the first equation instead of into the second.
It should be:
$7( 21-8y)+5y=14$
$ 147-56y+5y=14\quad$... add $-147$, simplify
$-51y=-133$
$y= \displaystyle \frac{133}{51}$
Substitute $y$ in $\quad x=21-8y.$
$x=21-8\displaystyle \cdot\frac{133}{51}$
$x=\displaystyle \frac{1071- 1064}{51}$
$x=\displaystyle \frac{7}{51}$
Solution: $(\displaystyle \frac{7}{51},\frac{133}{51})$
