[Math] Solve three simultaneous equations with three unknowns

Question

$0 = 9a + 3b + c$

$2 = 25a + 5b + c$

$6 = 49a + 7b + c$

These are my 3 equations that have 3 unknowns. How do I solve for these unknowns?

Answer 1

(1) $9a+3b+c=0$

(2) $25a+5b+c=2$

(3) $49a+7b+c=6$

Using (2)-(1) we have:

(4) $16a+2b=2$

Using (3)-(2) we have:

(5) $24a+2b=4$

Using (5)-(4) we have:

(6) $8a=2$

It follows that $a=\frac{1}{4}$, $b=-1$ and $c=\frac{3}{4}$.