Question

Using cross multiplication find the value of $x$ and $y$ for the equations:

$x-2y=4$ and $x-y=2$

• A. $x=0,y=-2$
• B. $x=0,y=2$
• C. $x=1,y=-2$
• D. $x=0,y=0$

Answer 1

The correct option is A $x=0,y=-2$

$x-2y=4$---(1)
$x-y=2$---(2)
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 (1) and (2) we can write the value of $a,b$ and $c$.
$\frac{x}{-2\times 2-(-1)\times 4}=\frac{y}{4\times 1-1\times 2}=\frac{-1}{1\times -1-1\times -2}$
$\frac{x}{-4+4}=\frac{y}{4-2}=\frac{-1}{-1+2}$
$\frac{x}{0}=\frac{y}{2}=\frac{-1}{1}$
$\frac{x}{0}=\frac{-1}{1}$
$1x=0$
$x=0$
$\frac{y}{2}=\frac{-1}{1}$
$y=-2$
Therefore, $x=0,y=-2$