Question

The coordinates of the point of intersection of the lines $ax+by=7$ and $bx+ay=5$ is $(3,1)$. Find the values of $a$ and $b$.

Answer 1

Two lines $ax+by=7$ and $bx+ay=5$ intersect at $(3,1)$

so, $(3,1)$ should satisfy both the lines. Hence,

$\Rightarrow 3a+b=\mathrm{7.....}\left(1\right)$

$3b+a=\mathrm{5....}\left(2\right)$

Solving the equations $\left(1\right)$ and $\left(2\right)$ simultaneously we can find the value of $a$ and $b,$

$Eq{u}^n\left(1\right)\times \mathrm{3.........9}a+3b=21$

$Eq{u}^n\left(2\right)\times \mathrm{1..........3}b+a=5$

subtracting we get : $8a=16$

$a=2$

$\therefore b=1$

Hence, the answer is $2,1.$