Question

Solve the equation by substitution method

0.2x+0.3y=1.3

0.4x+0.5y=2.3

Answer 1

Given equations: $0.2x+0.3y=1.3$ ...........(i)

$0.4x+0.5y=2.3\Rightarrow x=\frac{1}{0.4}(2.3-0.5y)$..........(ii)

Substitute equation(ii) in equation(i), we get

$\Rightarrow 0.2\left[\frac{1}{0.4}\right(2.3-0.5y\left)\right]+0.3y=1.3$

$\Rightarrow 0.5(2.3-0.5y)+0.3y=1.3$

$\Rightarrow 1.15-0.25y+0.3y=1.3$

$\Rightarrow 0.05y=1.3-1.15$

$\Rightarrow 0.05y=\frac{0.15}{0.05}$

$\therefore y=3$

Putting $y=3$ in the equation (ii), we get

$\Rightarrow x=\frac{1}{0.4}(2.3-0.5(3\left)\right)$.

$=\frac{1}{0.4}\left(0.8\right)$

$\therefore x=2$

Hence, $x=2,y=3$ is the solution of the equation.