Question

Solve $0.2x+0.3y=1.3$
$0.4x+0.5y=2.3$

• A. $x=-2$ and $y=3$
• B. $x=3$ and $y=3$
• C. $x=2$ and $y=3$
• D. None of these

Answer 1

Answer: (C)

$x=2$ and $y=3$

Let $0.2x+0.3y=1.3$ ....$\left(1\right)$

$0.4x+0.5y=2.3$ ....$\left(2\right)$

Multiply eqn$\left(1\right)$ by $10$ we get

$2x+3y=13$ ....$\left(3\right)$

Multiply eqn$\left(2\right)$ by $10$ we get

$4x+5y=23$ ....$\left(4\right)$

Solving equations $\left(3\right)$ and $\left(4\right)$

$5\times \left(3\right)\Rightarrow 10x+15y=65$

$3\times \left(4\right)\Rightarrow 12x+15y=69$

Subtracting we get $12x+15y-10x-15y=69-65=4$

or $2x=4$ or $x=2$

Substituting $x=2$ in eqn$\left(3\right)$ we get

$2x+3y=13\Rightarrow 2\times 2+3y=13$ or $3y=13-4=9$ or $y=3$

Hence $x=2,y=3$