Question

The number of common solutions for $4x-4y-7=0$ and $16x-16y=35$ is.

Answer 1

$4x-4y-7=0$ ...$\left(i\right)$

$16x-16y=35$ ....$\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$ [comparing with '$y=mx+c$']

$y=x-\frac{7}{4}$ ...$\left(ii\right)$

$y=x-\frac{35}{16}$ ...$\left(iv\right)$

Since in $\left(iii\right)$ and $\left(iv\right)$ the slopes are equal but the constant factor is different the two lines are parallel not coll near and hence never inter sect.

Therefore, they have no common solution.