Question

The equation $2x-3y+5=0$ and $6y-4x=10$ when solved simultaneously, have

• A. only one solution
• B. no solution
• C. only two solutions
• D. infinite number of solutions

Answer 1

Answer: (D)

infinite number of solutions

Given equations are $2x-3y=-5$ .... $\left(1\right)$
and $-4x+6y=10$ .... $\left(2\right)$
When we divide equation $\left(2\right)$ by $2$, we get
$-2x+3y=5$ .... $\left(3\right)$
We can see that both these equations $\left(1\right)$ and $\left(3\right)$ have the same coefficients of $x,y$ with same constants.
Thus, these equations represent same line.
Hence, these two equations have infinitely number of solutions.