SOLUTION: determine the value of p and q for which (–4,–3) will be solution of the system {px+qy=–26 {qx–py =7

The condition says:  substitute x= -4  and  y= -3  into the given system; then solve it for "p" and "q".


When you substitute, you will get

-4p -    3q = -26,
-4q - (-3)p =   7,

or, equivalently,


4p + 3q = 26,      (1)
3p - 4q =  7.      (2)


To solve it, multiply eq(1) by 3 (both sides) and nultiply eq(2) by 4 (both sides).  You will get

12p +  9q = 78,
12p - 16q = 28.
------------------------Now subtract eq(4) from eq(3)  (both sides). You will get

      25q = 78 - 28 = 50  ====>  q =  = 2.


Then from (2)  3p = 7 + 4q = 7 + 4*2 = 15  ====>  p =  = 5.


Answer.  p = 5,  q = 2.