The solution set of the pair of equations $x+y+1=0$ and $3x+3y+k=0$ is an infinite set. Then $k = \dots$

Solve the following pairs of equations:
$43x + 67y = -24$
$67x + 43y = 24$

Two numbers are in the ratio $5:6$. If $8$ is subtracted from each of the numbers,the ratio becomes $4:5$. Find the numbers.

Write a pair of linear equations which has the unique solution $x = -1, y = 3$. How many such pairs can you write?

Do the following pair of linear equations have no solution? Justify your answer.
$y + 6x = 6$ and $y = 2x$

In a competitive examination,one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$ marks. How many questions did she answer correctly?