Question

Solve the following pair of equations.

$4(x+2)+5(y+2)=20$ and $5x+4y=7$

• A. $x=7,y=-2$
• B. $x=4,y=-2$
• C. $x=3,y=-2$
• D. $x=2,y=-2$

Answer 1

Answer: (C)

$x=3,y=-2$

$4(x+2)+5(y+2)=20\Rightarrow 4x+5y=2$ ....(i)
$5x+4y=7$ ........(ii)
On adding (i) and (ii) , we get
$9x+9y=9$
$\Rightarrow x+y=1$ ....(iii)
On subtracting (i) from (ii) , we get
$x-y=5$ ....(iv)
On adding (iii) and (iv) , we get
$2x=6$
$\Rightarrow x=3$
By putting $x=3$ in (iv), we get
$3-y=5$
$\Rightarrow y=-2$
$\therefore x=3,y=-2$