Solve for x and y:
 
ax+by=c
bx+ay=+c

Asked by manojdedhia42 | 26th Aug, 2016, 12:31: AM

Expert Answer:

begin mathsize 16px style a x space plus b y equals c space space space space space space left parenthesis 1 right parenthesis
b x plus a y equals 1 plus c space space space space space space left parenthesis 2 right parenthesis
M u l t i p l y i n g space left parenthesis 1 right parenthesis space b y space a comma space w e space g e t
a squared x plus a b y equals a c space space space space space left parenthesis 3 right parenthesis
M u l t i p l y i n g space left parenthesis 2 right parenthesis space b y space b comma space w e space g e t
b squared x plus a b y equals b plus b c space space space space space space space left parenthesis 4 right parenthesis
S u b t r a c t i n g space left parenthesis 4 right parenthesis space f r o m space left parenthesis 3 right parenthesis comma
left parenthesis a squared minus b squared right parenthesis x equals left parenthesis a minus b right parenthesis c minus b
rightwards double arrow x equals fraction numerator left parenthesis a minus b right parenthesis c minus b over denominator left parenthesis a squared minus b squared right parenthesis end fraction equals fraction numerator left parenthesis a minus b right parenthesis c over denominator left parenthesis a squared minus b squared right parenthesis end fraction minus fraction numerator b over denominator left parenthesis a squared minus b squared right parenthesis end fraction equals fraction numerator c over denominator a plus b end fraction minus fraction numerator b over denominator a squared minus b squared end fraction
S u b s t i t u t i n g space x space i n space left parenthesis 1 right parenthesis comma
a open parentheses fraction numerator c over denominator a plus b end fraction minus fraction numerator b over denominator a squared minus b squared end fraction close parentheses plus b y equals c
rightwards double arrow b y equals c minus fraction numerator a c over denominator a plus b end fraction plus fraction numerator a b over denominator a squared minus b squared end fraction
rightwards double arrow b y equals fraction numerator a c plus b c space minus a c over denominator a plus b end fraction plus fraction numerator a b over denominator a squared minus b squared end fraction
rightwards double arrow b y equals fraction numerator b c over denominator a plus b end fraction plus fraction numerator a b over denominator a squared minus b squared end fraction
rightwards double arrow y equals fraction numerator c over denominator a plus b end fraction plus fraction numerator a over denominator a squared minus b squared end fraction end style

Answered by Rashmi Khot | 26th Aug, 2016, 04:32: PM