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Harish Uthaya kumar

May 5, 2014

ax+by=c and ay+bx=c+1 find the value of x and y

Sagar kumar

Given equations are ax+by = c --------------(1) and ay+bx = c+1 --------------(2)

multiply equation (1) by 'b' and equation (2) by 'a' we get

abx+b^{2}y = bc

abx +a^{2}y= ac+a (substract)

------------------------------------

( b^{2}-a^{2})y = bc - ac -a

y = (bc - ac -a) / ( b^{2}-a^{2})^{ }

multiply equation (1) by 'a' and equation (2) by 'b' we get

a^{2}x+aby = ac

aby+b^{2}x = bc+b (substract)

---------------------------

(a^{2}- b^{2})x = (ac-bc -b)

x = (ac-bc -b) / (a^{2}- b^{2})

∴ the values of x and y are (ac-bc -b) / (a^{2}- b^{2}) , (bc - ac -a) / ( b^{2}-a^{2})^{ }.

multiply equation (1) by 'b' and equation (2) by 'a' we get

abx+b

abx +a

------------------------------------

( b

y = (bc - ac -a) / ( b

multiply equation (1) by 'a' and equation (2) by 'b' we get

a

aby+b

---------------------------

(a

x = (ac-bc -b) / (a

∴ the values of x and y are (ac-bc -b) / (a

Raghunath Reddy

Sol :

Given equations are ax+by = c --------------(1) and ay+bx = c+1 --------------(2)

multiply equation (1) by 'b' and equation (2) by 'a' we get

abx+b^{2}y = bc

abx +a^{2}y= ac+a (substract)

------------------------------------

( b^{2}-a^{2})y = bc - ac -a

y = (bc - ac -a) / ( b^{2}-a^{2})^{ }

multiply equation (1) by 'a' and equation (2) by 'b' we get

a^{2}x+aby = ac

aby+b^{2}x = bc+b (substract)

---------------------------

(a^{2}- b^{2})x = (ac-bc -b)

x = (ac-bc -b) / (a^{2}- b^{2})

∴ the values of x and y are (ac-bc -b) / (a^{2}- b^{2}) , (bc - ac -a) / ( b^{2}-a^{2})^{ }.

Given equations are ax+by = c --------------(1) and ay+bx = c+1 --------------(2)

multiply equation (1) by 'b' and equation (2) by 'a' we get

abx+b

abx +a

------------------------------------

( b

y = (bc - ac -a) / ( b

multiply equation (1) by 'a' and equation (2) by 'b' we get

a

aby+b

---------------------------

(a

x = (ac-bc -b) / (a

∴ the values of x and y are (ac-bc -b) / (a