Back substitution mathematics

Question

Use back substitution to solve the following equations:

2x - y = -7

2y +  2z = 12

3z = 9

Answer = z = 3, y = 3, x = -2

How do i get these answers? Could anyone explain clearly?

Thanks

Answer 1

We are given the following three equations:

a) $2x - y = -7$;

b) $2y + 2z = 12$;

c) $3z = 9$.

Dividing both sides of equation c) by 3 yields $z = 3$. Then substituting $z=3$ into equation b) gives us $2y + 2(3) = 12$ and hence $2y = 6$ and so dividing both sides by $2$ we get $y=3$. Finally, plugging $y=3$ into equation a) we have $2x - 3 = -7$ so $2x = -4$ and hence, again dividing both sides by $2$, $x=-2$.