Question

Solutions of the pair of equations $2x+5y=3$ and $3x-2y=1$
using elimination method is

• A. $(\frac{11}{19},\frac{7}{19})$
• B. $(\frac{11}{19},\frac{3}{19})$
• C. $(\frac{7}{19},\frac{3}{19})$
• D. $(-\frac{11}{19},\frac{7}{19})$

Answer 1

The correct option is A $(\frac{11}{19},\frac{7}{19})$

Given equations :
$2x+5y=3\dots \left(1\right)$
$3x-2y=1\dots \left(2\right)$
Multiply by $2$ in equation $\left(1\right)$ and by $5$ in equation $\left(2\right)$
$4x+10y=6\dots \left(3\right)$
$15x-10y=5\dots \left(4\right)$
Now, adding equations $\left(3\right)$ and $\left(4\right)$ to eliminate $y$.

$4x+10y=6$
$\underset{–}{15x-10y=5}$
$19x=11$

We get,
$19x=11$
$\Rightarrow x=\frac{11}{19}$
Plugging $x=\frac{11}{19}$ into equation $\left(1\right)$
$2\times \frac{11}{19}+5y=3$
$\frac{22}{19}+5y=3$
$5y=\frac{57}{19}-\frac{22}{19}=\frac{35}{19}$
$\Rightarrow y=\frac{7}{19}$