Question

Solve the following pair of linear equations by cross multiplication method

$0.3x+0.4y=2.5$ and $0.5x-0.3y=0.3$

• A. $x=-3$ and $y=4$
• B. $x=3$ and $y=4$
• C. $x=4$ and $y=-4$
• D. None of these

Answer 1

The correct option is B $x=3$ and $y=4$

$0.3x+0.4y=2.5$ and $0.5x-0.3y=03$

$3x+4y=25$ and $5x-3y=3$

$3x+4y=25\Rightarrow 3x+4y-25=0$

$5x-3y=3\Rightarrow 5x-3y-3=0$

$\frac{x}{b_1{c}_2-b_2{c}_1}=\frac{y}{c_1{a}_2-a_1{c}_2}=\frac{1}{a_1{b}_2-a_2{b}_1}$

$\frac{x}{\left(4\right)(-3)-(-3)(-25)}=\frac{4}{(-25)\left(5\right)-(-3)\left(3\right)}=\frac{1}{\left(3\right)(-3)-\left(5\right)\left(4\right)}$

$\frac{x}{-12-75}=\frac{y}{-125+9}=\frac{1}{-9-20}$

$x=\frac{-87}{-29}=3$

$y=\frac{-116}{-29}=4$

$\therefore x=3,y=4$