Question

Solve the following pair of linear equation by the substitution method.
$0.2x+0.3y=1.3$
$0.4x+0.5y=2.3$

Answer 1

Given

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

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

from equation $\left(1\right)$

$x=\frac{1.3-0.3y}{0.2}$

substitute $x$ in equation $\left(2\right)$

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

$\frac{0.5\times 2-0.12y}{0.2}+0.5y=2.3$

$\frac{0.5\times 2-0.12y+0.10y}{0.2}=2.3$

$0.52-0.12y+0.10y=0.46$

$-0.02y=0.46-0.52$

$-0.02y=0.06$

$y=\frac{0.06}{0.02}$

$y=3$

Substitute $y=3$ in $x$

$x=\frac{1.8-0.3\left(3\right)}{0.2}$

$=\frac{1.3-0.9}{0.2}$

$=\frac{0.4}{0.2}$

$=2$

$\therefore x=2,y=3$