jika garis (a+b)x +2by=2 dan garis ax-(-b-3a)y=-4 berpotongan (1,-1) hitunglah nilai a+b

jawab

(a+b) x + (2b) y = 2 ...(i)
(a) x - (-b-3a) y = - 4....(ii)

(x,y) = (1 ,-1) x = 1 , y1= -1
subke (i)
(a+b)(1) + 2b(-1) = 2
a + b - 2b = 2
a - b = 2...(iii)

sub ke (ii)
(a) (1) - (-b-3a)(-1) = -4
a -  b - 3a = - 4
-2a - b = - 4 ...(iv)

(iii) dan (iv)
a -  b = 2
-2a - b = -4 || (-)
3a = 6
a = 2

a - b = 2
b = a - 2
b = 0

a +b = 2

Persamaan Garis Lurus.

(x, y) = (1, -1)
(a + b)x + 2by = 2
(a + b)(1) + 2b(-1) = 2
a - b = 2

ax - (-b - 3a)y = -4
a(1) - (-b - 3a)(-1) = -4
a - (b + 3a) = -4
-2a - b = -4

a - b = 2
-2a - b = -4
-------------- -
3a = 6 → a = 2
2 - b = 2 → b = 0

a + b = 2 + 0 = 2