Prove that the straight lines y - x + 1 = 0, 2y - x - 1 = 0 and 7x -y - 19 = 0 are concurrent.

Without solving the equations show that the straight lines 4x - y + 2 = 0, 3x + 2y -1 = 0 and x - 3y + 3 = 0 are concurrent.

Find the value of m for which the lines 4x -3y - 1 = 0, 3x - 4y + 1 = 0 and mx - 7y + 3 = 0 are concurrent.

Find the equation of straight line passing through the point of intersection of the straight lines 2x - 3y + 4 = 0 and x + 2y - 5 = 0 and perpendicular to the line 3x - 4y + 5 = 0.

A straight line passes through the point of intersection of the straight lines 3x - 2y + 4 = 0 and 2x + 3y +5 = 0 and is parallel to the straight line x -y + 5 = 0. Find its equation.

Show that the straight line 3x + 4y = 20 touches the circle x ^2 + y ^2 = 16.

Examine whether the circles x ^2 + y ^2 - 2x - 4y = 0 and x ^2 + y ^2 - 8y - 4 = 0 touch each other.

For what value of c, the straight line 3x + y - c = 0 touches the circle x ^2 + y ^2 + 2x - 6y + 6 = 0 ?

Find the equation of the straight line passing through the point (3, 2) and the point of intersection of the lines 3x + 2y - 1 = 0 and x - 3y + 5 = 0.