Question

Choose the correct answer from the alternatives given.
If $\frac{x+y-8}{2}=\frac{x+2y-14}{3}=\frac{3x+y-12}{11}$ then find the values of x and y, respectively.

• A. $2,6$
• B. $4,8$
• C. $3,5$
• D. $4,5$

Answer 1

The correct option is A $2,6$

Given that
$\frac{x+y-8}{2}=\frac{x+2y-14}{3}$
$3x+3y-24=2x+4y-28$
$x-y=-4$ ....... (1)
and $\frac{x+y-8}{2}=\frac{3x+y-12}{11}$
$11x+11y-88=6x+2y-24$
$5x+9y=64$ ....... (2)

Multiply (1)by 9

$9x-9y=-36$..................(3)

adding (2) and (3)

$14x=28$

$x=\frac{28}{14}=2$

put value of x in (1)

$2-y=-4$

$-y=-4-2$

$-y=-6$

$y=6$

we get $x=2,y=6$