Point of intersection of family of lines given by 3x+4y−7+λ5x−2y−3=0 is

The point of intersection of family of lines given is same as the point of intersection of the lines  3x+4y−7=0,5x−2y−3=0Eliminate  y3x+4y−7+25x−2y−3=03x+4y−7+10x−4y−6=013x−13=0x=1  Substitute x=1 in the equation  5x−2y−3=0 to get the y coordinate  51−2y−3=0−2y+2=0y=1Therefore, the point of intersection of family of lines is  1,1