Alg3.1.6

Solve the equations by eliminating x in $3x-5y=1,5x+2y=19\,$

Given $3x-5y=1,5x+2y=19\,$

Let the two equations be 1 and 2 respectively.To eliminate x, the coefficients in the two equations to be made equal.

Hence multiplying the first by 5 and the second by 3,we get

$5(3x-5y)=5,3(5x+2y)=57\,$

$15x-25y=5,15x+6y=57\,$

Subtracting 2 from 1,we have

$(15x-25y-5)-(15x+6y-57)=0\,$

$-25y-6y-5+57=0,y=\frac{52}{31}\,$

$3x-5(\frac{52}{31})=1,3x=1+\frac{260}{31},3x=\frac{291}{31},x=\frac{97}{31}\,$