Question

Find the solution of the form $x=a,y=0$ and $x=0$, $y=b$ for the following equation:
$2x+5y=10$ and $2x+3y=6$
Is there any common solution?

Answer 1

$\Rightarrow$ $2x+5y=10$

Now, put $x=a$ and $y=0$

$\Rightarrow$ $2\left(a\right)+5\left(0\right)=10$

$\Rightarrow$ $2a=10$

$\Rightarrow$ $a=\frac{10}{2}$

$\therefore$ $a=5$

$\Rightarrow$ Now, $2x+3y=6$

substituting $x=0$ and $y=b$

$\Rightarrow$ $2\left(0\right)+3\left(b\right)=6$

$\Rightarrow$ $3b=6$

$\Rightarrow$ $b=\frac{6}{3}$

$\Rightarrow$ $b=2$