Question

Solve

$x=-y+6$
$2(x+y)=4-3y$

• A. $\frac{13}{3},\frac{-5}{3}$
• B. $\frac{26}{3},\frac{8}{3}$
• C. $\frac{26}{3},\frac{-8}{3}$
• D. $\frac{-16}{3},\frac{7}{3}$

Answer 1

The correct option is C $\frac{26}{3},\frac{-8}{3}$

$x=-y+6$

$\Rightarrow$ $x+y=6$ --- ( 1 )

$2(x+y)=4-3y$

$\Rightarrow$ $2x+2y=4-3y$

$\Rightarrow$ $2x+5y=4$ ----- ( 2 )

Multiplying eqaution ( 1 ) by $2$,

$\Rightarrow$ $2x+2y=12$ ---- ( 3 )

Subtracting eqation ( 2 ) from ( 3 ) we get,

$\Rightarrow$ $-3y=8$

$\therefore$ $y=\frac{-8}{3}$

Substituting value of $y$ in equation ( 1 ),

$\Rightarrow$ $x+\left(\frac{-8}{3}\right)=6$

$\Rightarrow$ $x=6+\frac{8}{3}$

$\Rightarrow$ $x=\frac{18+8}{3}$

$\therefore$ $x=\frac{26}{3}$

$\therefore$ $(x,y)=(\frac{26}{3},\frac{-8}{3})$