Simultaneous Equations from Quadratic Formula without Calculator

Question

From $ax^2+bx+c$ (quadratic formula) $3$ points $(5,500), (3,375), (12,980)$ I solved $$25a+5b+c=500$$ $$9a+3b+c=375$$ $$144a+12b+c=980$$ My question: Is it possible to solve it without a calculator (for the simulateneous equations) If yes, How can I do it?

Answer 1

$$25a+5b+c=500 \tag 1$$ $$9a+3b+c=375\tag 2$$ $$144a+12b+c=980\tag 3$$ $$(1)-(2) \implies 16a+2b=125 \tag 4$$ $$(3)-(1) \implies 119a+7b=480 \tag 5$$ $$7 \times (4)\implies 112a+14b=875\tag 6$$ $$2 \times (5)\implies 238a+14b=960\tag 7$$ $$(7)-(6) \implies 126a=85 \implies a=\frac{85}{126}$$ Go back to $(4)$ to get $b$ and then to $(1)$ to get $c$.