Question

Solve: $\frac{x+y}{2}+\frac{3x-5y}{4}=2,\frac{x}{14}+\frac{y}{18}=1$

• A. $7,8$
• B. $7,9$
• C. $6,10$
• D. None

Answer 1

The correct option is B $7,9$

Given,
$\frac{x+y}{2}+\frac{3x-5y}{4}=2$.............Eq(1)
$\frac{x}{14}+\frac{y}{18}=1$....................Eq(2)
On solving eq (1) we get
$\frac{x+y}{2}+\frac{3x-5y}{4}=2$
$\Rightarrow \frac{2(x+y)+(3x-5y)}{4}=2$
$\Rightarrow 2x+2y+3x-5y=8$
$\Rightarrow 5x-3y=8$.............................Eq(3)..multiplied by 7
on solving Eq(2) we get
$\frac{x}{14}+\frac{y}{18}=1$
$\Rightarrow \frac{9x+7y}{126}=1$
$\Rightarrow 9x+7y=126$..........................Eq(4)...multipied by3
on adding both Eq 3 and Eq 4 we get
$35x-21y=56$
$27x+21y=378$
_________________________
$62x=434$
$x=\frac{434}{62}=7$
putting the value of x=7 in eq 4 we get
$9\times 7+7y=126$
$7y=126-63$
$7y=63$
$y=\frac{63}{7}=9$
Hence x=7 and y=9