Solve y+1=2y-1 and represent the solution on the coordinate plane.

Solve the equations 3y+2=y-8 and represent the solution in the number line.

Solve the equation 2x + 1 = x - 3, and represent the solution(s) on (i) the number line, (ii) the Cartesian plane.

If (x+1,x) and (6,y-2) represent the same point in cartesian plane, then find x and y.

The coordinates of points in the table: represent some of the solutions of the equations x+y+2=0

Find the coordinates of the foot of the perpendicular and the perpendicular distance of the point P (3, 2, 1) from the plane 2x - y + z + 1 = 0. Find also, the image of the point in the plane.

The differential equation of all circle in the first quadrant touch the coordinate is (a) (x-y)^(2)(1+y')^(2)=(x+yy')^(2) (b) (x-y)^(2)(1+y')^(2)=(x+y')^(2) ( c ) (x-y)^(2)(1+y')=(x+yy')^(2) (d) None of these

The line of greatest slope on an inclined plane P_1 is the line in the plane P_1 which is perpendicular to the line of intersection of the plane P_1 and a horizontal plane P_2 . Q. The coordinate of a point on the plane 2x+y-5z=0, 2sqrt(11) unit away from the line of intersection of 2x+y-5z=0 and 4x-3y+7z=0 are

Statement 1: The lines (x-1)/1=y/(-1)=(z+1)/1 and (x-2)/2=(y+1)/2=z/3 are coplanar and the equation of the plnae containing them is 5x+2y-3z-8=0 Statement 2: The line (x-2)/1=(y+1)/2=z/3 is perpendicular to the plane 3x+5y+9z-8=0 and parallel to the plane x+y-z=0

Solve the following pairs of equations by reducing them to a linear pair :- 1/2x - 1/y = -1 , 1/x+1/2y = 8 .

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2 equals