maths help?

Question

stuck on this question

the line "l" with the equation 3x+y - 9 = 0 intersects the line "m" wth the equation 2x+3y-12=0 at the point A
a) Find, as exact fractions, the coordinates of the point A

the region r1 is bounded by l, m and the y axis
the region r 2 is bounded by l, m and the x axis

b) show that the ratio of the are of r2 is 25:18

thanks

Answer 1

3x + y - 9 = 0 so y = 9 - 3x
2x + 3y -12 = 0 = 2x + 3(9 - 3x) -12 = 27 - 12 + 2x - 9x = 15 -7x

x = 15/7
y = (63 - 45)/7 = 18/7

b) l crosses the axes at the points (0, 9) and (3,0)
m crosses at (6,0) and (0,4)

The areas are 1/2 base x height

Area r1 = 1/2 x (9 - 4) x 15/7 = (3 x 5 x 5) / (2 x 7)

Area r2 - 1/2 x (6 - 3) x 18/7 = (3 x 18) / (2 x 7)

ratio r1:r2 = 25:18