Menu Close

solve-the-pairs-of-simultaneous-equations-ax-2y-2-x-3y-3-qy-px-q-2-p-2-pq-py-qx-2-




Question Number 156244 by Eric002 last updated on 09/Oct/21
solve the pairs of simultaneous equations  ax−2y=2  x+3y=3  qy−px=(q^2 −p^2 )/pq  py+qx=2
$${solve}\:{the}\:{pairs}\:{of}\:{simultaneous}\:{equations} \\ $$$${ax}−\mathrm{2}{y}=\mathrm{2} \\ $$$${x}+\mathrm{3}{y}=\mathrm{3} \\ $$$${qy}−{px}=\left({q}^{\mathrm{2}} −{p}^{\mathrm{2}} \right)/{pq} \\ $$$${py}+{qx}=\mathrm{2} \\ $$
Answered by MJS_new last updated on 10/Oct/21
(1) x=((12)/(3a+2))∧y=((3a−2)/(3a+2))∧a≠−(2/3)  (2) x=((p^2 +2pq−q^2 )/(2pq^2 ))∧y=−((p^2 −2pq−q^2 )/(2p^2 q))∧p≠0∧q≠0
$$\left(\mathrm{1}\right)\:{x}=\frac{\mathrm{12}}{\mathrm{3}{a}+\mathrm{2}}\wedge{y}=\frac{\mathrm{3}{a}−\mathrm{2}}{\mathrm{3}{a}+\mathrm{2}}\wedge{a}\neq−\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{2}\right)\:{x}=\frac{{p}^{\mathrm{2}} +\mathrm{2}{pq}−{q}^{\mathrm{2}} }{\mathrm{2}{pq}^{\mathrm{2}} }\wedge{y}=−\frac{{p}^{\mathrm{2}} −\mathrm{2}{pq}−{q}^{\mathrm{2}} }{\mathrm{2}{p}^{\mathrm{2}} {q}}\wedge{p}\neq\mathrm{0}\wedge{q}\neq\mathrm{0} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *