Question

Find the solution of $x$ and $y$ using cross multiplication method:

$6x-5y=9$ and $x-y=2$

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

Answer 1

Answer: (D)

$x=-1,y=-3$

$6x-5y=9$---$\left(1\right)$
$x-y=2$---$\left(2\right)$
Using formula for cross multiplication method:
$\frac{x}{(b_1{c}_2-b_2{c}_1)}=\frac{y}{(c_1{a}_2-a_1{c}_2)}=\frac{-1}{(a_1{b}_2-a_2{b}_1)}$
So, from equation $\left(1\right)$ and $\left(2\right)$ we can write the value of $a,b$ and $c$.
$\frac{x}{(-5)\times 2-(-1)\times 9}=\frac{y}{9\times 1-6\times 2}=\frac{-1}{6\times (-1)-1\times (-5)}$
$\frac{x}{-10+9}=\frac{y}{9-12}=\frac{-1}{-6+5}$
$\frac{x}{-1}=\frac{y}{-3}=\frac{-1}{-1}$
$\frac{x}{-1}=\frac{-1}{-1}$
$-x=1$
$x=-1$
$\frac{y}{-3}=\frac{-1}{-1}$
$y=-3$
Therefore, $x=-1,y=-3$