Please help me with this algebra problem.

$x+14y=84$

$2x-7y=-7$

In the first equation, solve for $x$

$x-14y=84$

add $14y$ to both sides

$x=84+14y$

Now subsitute $84+14y$ in the second equation where you see x

$2(84+14y)-7y=-7$

Distribute the $2$

$168+28y-7y=-7$

Now add $28y$ and $-7$ together

$168+21y=-7$

Now subtract $168$ from both sides

$21y=-175$

Now divide $21$ to both sides

$y=\frac{-25}{3}$

$y=-\frac{25}{3}$

In decimal form

$y=-8.333333...$

Solve the following system:
{x+14 y = 84
2 x-7 y = -7

In the first equation, look to solve for x:
{x+14 y = 84
2 x-7 y = -7

Subtract 14 y from both sides:
{x = 84-14 y
2 x-7 y = -7

Substitute x = 84-14 y into the second equation:
{x = 84-14 y
2 (84-14 y)-7 y = -7

2 (84-14 y)-7 y = (168-28 y)-7 y = 168-35 y:
{x = 84-14 y
168-35 y = -7

In the second equation, look to solve for y:
{x = 84-14 y
168-35 y = -7

Subtract 168 from both sides:
{x = 84-14 y
-35 y = -175

Divide both sides by -35:
{x = 84-14 y
y = 5

Substitute y = 5 into the first equation:
Answer: | {x = 14    y = 5