Question

in the system of linear equations below, q and r are constants. the solution to the system is (-1, 4).

qx-ry=18

rx+qy=13

What are the values of q and r

Answer 1

if x is -1 and y is 4:

-1q + 4r = 18 <--- Equation 1

-1r + 4q = 13 <--- Equation 2

Lets take the first eq, and separate q (or make it subject):

-1q = 18 - 4r

q = (18 - 4r) / -1

q = -18 + 4r

q = 4r - 18 <--- Equation 3

Now we will replace 'q' with the value of 'q' that we simplified in Equation 3, in the second equation.

-1r + 4(4r - 18) = 13

16r - 72 - r = 13

15r = 85

r = 17/3

Now put the value of r in equation 3,

q = 4 (17/3) - 18

q = 14/3