Question

Jika garis k dengan persamaan (x +2y) + ( x + by) = a berhimpit dengan garis g dengan persamaan (5x + y) - 3a(x + y) = 2a maka nilai a + b adalah

Answer 1

Verified answer

(x +2y) + (x + by) = a
x + 2y + x + by = a
2x + 2y + by = s
2x + (2 +b) y = a
(2+b)y = -2x + a
y = (-2x + a)/(2+b)
y = (-2/(2+b)x + a/(2+b)...(1)
(5x+y) -3(x+y) = 2a
5x + y -3x -3y = 2a
2x -2y = 2a
x - y = a
y = x - a....(2)
Karena garis berimpit maka kedua garis sama.
maka => (-2/(2+b) = 1
-2 = 2+b
b = -2 -2 = -4
=> a/(2+b) = -1..,subsitudikan b = -4
a/(2+-4) = -1
a/-2 = -1
a = -1× -2
a = 2
a + b = 2 + -4 = -2