Question

find the value of x and y 3x-5y=1 and 5x+2y=19​

Answer 1

${3x}-{5y}-{1}={0}$ ____( i )

${5x}+{2y}-{19}={0}$ ____( ii )

MULTIPLYING EQ. ( i ) FROM 2 AND EQ. ( ii ) FROM 5, WE GET:-

${6x}-{10y}-{2}={0}$ ____( iii )

${25x}+{10y}-{95}={0}$ ____( iv )

ADDING EQ. ( iii ) FROM EQ. ( iv ):-

${25x}+{10y}-{95}={0}$

(+) ${6x}-{10y}-{2}={0}$

________________________

${31x}-{97}={0}$

${x} =\frac{97}{31}$

SUBSTITUTING VALUE OF x IN EQ. ( i ):-

${3}×\frac{97}{31}-{5y}-{1}={0}$

$\frac{291}{31}-{5y}={1}$

${-5y}={1}-\frac{291}{31}$

${-5y}=\frac{(31-291)}{31}$

${-5y}=\frac{(31-291)}{31}$

${-5y}=\frac{-260}{31}$

${y}=\frac{260}{31×5}$

${y}=\frac{52}{31}$

ANSWER:-

${x}=\frac{97}{31}$

${y}=\frac{52}{31}$