Question

Solve the following pair of linear equations by the substitution method.

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

• A. $x=1,y=-2$
• B. $x=6,y=-7$
• C. $x=5,y=1$
• D. $x=2,y=3$

Answer 1

The correct option is D $x=2,y=3$

The given equations are
$\Rightarrow .2x+.3y=\mathrm{1.3........}eq1$
$\Rightarrow x=\frac{1.3-.3y}{.2}.......eq2$

and
$\Rightarrow .4x+.5y=\mathrm{2.3.......}eq3$
Substitute the value of x in eq3
$\Rightarrow .4\times \left(\frac{1.3-.3y}{.2}\right)+.5y=2.3$
$\Rightarrow 2.6-.6y+.5y=2.3$
$\Rightarrow -.1y=-.3\Rightarrow y=3$
Substitute $y=3$ in eq 2
$\Rightarrow x=\frac{1.3-.9}{.2}\Rightarrow x=2$
Hence x=2 and y=3