Question

Solve the following pair of linear equations by elimination method

$\frac{x}{2}+\frac{2y}{3}=-1$ and $x-\frac{y}{3}=3$

• A. $x=1,y=7$
• B. $x=2,y=-3$
• C. $x=3,y=-3$
• D. $x=5,y=-7$

Answer 1

Answer: (B)

$x=2,y=-3$

Given system of equations are:
$\frac{x}{2}+\frac{2y}{3}=-1$......(1)
$x-\frac{y}{3}=3$................(2)
From eq 1 will have
$\Rightarrow 3x+4y=-6.$........(3)
From eq 2 will have
$\Rightarrow 3x-y=9$...........(4)

Now using elimination method frist we will eliminate y :
now multiplying eq 4 from 4 will have
$\Rightarrow 12x-4y=36$
Now from eq 3 and 4 will get x:
$3x+4y=-6$
$12x-4y=36$
$\Rightarrow 15x=30$
$\Rightarrow x=2$
Now substituting $x=2$ in eq 2 will get y
$\Rightarrow \left(2\right)3-y=9$
$\Rightarrow 6-y=9$
$\Rightarrow -y=9-6$
$\Rightarrow y=-3$
$\Rightarrow x=2,y=-3$