Question

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

$4x+3y=8$ and $4x+5y=12$

• A. $x=\frac{1}{2}$, $y=2$
• B. $x=\frac{3}{2}$, $y=2$
• C. $x=\frac{1}{2}$, $y=-2$
• D. $x=\frac{1}{2}$, $y=1$

Answer 1

The correct option is A $x=\frac{1}{2}$, $y=2$

$4x+3y=8$---(1)
$4x+5y=12$---(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 $c$.
$\frac{x}{3\times 12-5\times 8}=\frac{y}{8\times 4-4\times 12}=\frac{-1}{4\times 5-4\times 3}$
$\frac{x}{36-40}=\frac{y}{32-48}=\frac{-1}{20-12}$
$\frac{x}{-4}=\frac{y}{-16}=\frac{-1}{8}$
$\frac{x}{-4}=\frac{-1}{8}$
$x=\frac{4}{8}=\frac{1}{2}$
$\frac{y}{-16}=\frac{-1}{8}$
$8y=16$
$y=2$
Therefore, $x=\frac{1}{2}$, $y=2$