Question

Find the number of solutions of simultaneous linear equations:
$9y=15x+3$
$6y=10x+4$

• A. No solution
• B. Infinitely many solution
• C. Unique solution
• D. None of the above

Answer 1

The correct option is A No solution

Given equations are:
$9y=15x+3$ $.....\left(1\right)$
$6y=10x+4$ $.....\left(2\right)$
Simplifying both equation by dividing $3$ in equation $\left(1\right)$ and $2$ in equation $\left(2\right)$ both sides.
$\Rightarrow \frac{9y}{3}=\frac{15x+3}{3}$ (From equation $1$)
$\Rightarrow 3y=5x+1\Rightarrow y=\frac{5}{3}x+\frac{1}{3}$
And,
$\Rightarrow \frac{6y}{2}=\frac{10x+4}{2}$ (From equation $2$)
$\Rightarrow 3y=5x+2\Rightarrow y=\frac{5}{3}x+\frac{2}{3}$.
Clearly, Slope for both the lines are same, Only y-intercept is different.
On plotting on cartesian coordinate we get,


​​​​​​Since, both lines are parallel to each other and they never intersect.
So, their will be No solution.