Question

In the system of equations $4(x+3)-3(y+1)=4$ and $3(x-1)+(2y-3)=20$, the values of $x$ and $y$ are:

• A. $4$ and $7$
• B. $5$ and $7$
• C. $9$ and $4$
• D. $2$ and $5$

Answer 1

The correct option is A $4$ and $7$

$\because 4(x+3)-3(y+1)=4$
$\Rightarrow 4x+12-3y-3=4$
$\Rightarrow 4x-3y=-5$ ...(1)
and $3(x-1)+(2y-3)=20$
$\Rightarrow 3x-3+2y-3=20$
$\Rightarrow 3x+2y=26$ ...(ii)
On multiplying equation (i) by 2 and equation(ii) by 3 and adding the two together,
$\therefore 2(4x-3y)+3(3x+2y)=-5\times 2+26+3$
$\therefore 8\times -6y+9x+6y=-10+78$
$\Rightarrow 17x=68$
$\therefore x=\frac{68}{17}=4$
On substituting this value of x in equation (i),
$4\times 4-3y=-5\Rightarrow 3y=16+5=21$
$\therefore y=\frac{21}{3}=7\therefore x=4,y=7$