Question

Solve for $x$ and $y$ in $8x-7y=19$ and$10x-9y=23$.

• A. $x=5,y=3$
• B. $x=-5,y=3$
• C. $x=-5y=-3$
• D. none

Answer 1

The correct option is A $x=5,y=3$

The given equation are,

$8x-7y=19$ ----- ( 1 )

$10x-9y=23$ ---- ( 2 )

Multiplying equation ( 1 ) by $10$ and equation ( 2 ) by $8$ we get,

$\Rightarrow$ $80x-70y=190$ ---- ( 3 )

$\Rightarrow$ $80x-72y=184$ ----- ( 4 )

Subtracting equation ( 4 ) from ( 3 ) we get,

$\Rightarrow$ $2y=6$

$\therefore$ $y=3$

Substituting value of $y=3$ In equation ( 1 ) we get,

$\Rightarrow$ $8x-7\left(3\right)=19$

$\Rightarrow$ $8x-21=19$

$\Rightarrow$ $8x=40$

$\therefore$ $x=50$

$\therefore$ $x=5,y=3$