document.write( "Question 990836: The lines x-y-2=0 and 2x-5y-7=0 intersect at point P. Find co-ordinates of point P. The line through P with gradient 2 meets the axis A and B. Calculate the area of triangle AOB. \n" ); document.write( "
Algebra.Com's Answer #612439 by anand429(138)![]() ![]() You can put this solution on YOUR website! x-y-2=0 ---(i) \n" ); document.write( "2x-5y-7=0---- (ii) \n" ); document.write( "Multiplying eqn (i) by 2, \n" ); document.write( "2x-2y-4=0 ---(iii) \n" ); document.write( "Subtracting (ii) from (iii), we get, \n" ); document.write( "3y+3=0 \n" ); document.write( "=> y = -1 \n" ); document.write( "Putting back, x= y+2 = 1 \n" ); document.write( "So, intersection pt. P is (1,-1) \n" ); document.write( "Let the line through P with gradient 2 be given by, \n" ); document.write( "y = 2x + c \n" ); document.write( "Since it passes through P(1,-1) \n" ); document.write( "-1 = 2*1 + c \n" ); document.write( "=> c = -3 \n" ); document.write( "So the required line is \n" ); document.write( "y = 2x - 3 \n" ); document.write( "For finding intersection with axes, putting x and y =0 separately, we get, the intersection points as A(0,-3) and B(3/2,0) \n" ); document.write( "So, area of triangle OAB \n" ); document.write( "= (1/2)*(3)*(3/2) \n" ); document.write( "= 9/4 sq. units. \n" ); document.write( " |