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3Y = 4X + 10 => Y = 4X/3 + 10/3
4Y + 5X = 4: 4Y = 4 - 5X: Y = 1 - 5X/4
Y = Y:
4X/3 + 10/3 = 1 - 5X/4
4X/3 + 5X/4 = 1 - 10/3
4X/3 + 5X/4 = [4(4X) + 3(5X)]/12 = [16X + 15X]/12 = 31X/12
1 - 10/3 = 3/3 - 10/3 = -7/3
31X/12 = -7/3
31X(3) = -7(12)
93X = -84
X = -84/93 = -28/31
X = -28/31
Y = 1 - 5X/4
Y = 1 - 5(-28/31)/4
Y = 1 + 35/31
Y = 31/31 + 35/31 = 66/31
Punto de corte (-28/31 , 66/31)
Sea Ф = Al angulo que forman las dos rectas
TanФ = [(m2 - m1)/(1 + m2m1)]
Donde m1 = 4/3; m2 = -5/4
m2 - m1 = -5/4 - 4/3 = -31/12
m2m1 = (-5/4)(4/3) = (-5x4)/(4x3) = -5/3
1 + (-5/3) = 1 - 5/3 = 3/3 - 5/3 = -2/3
TanФ = [(-31/12)/(-2/3)]
TanФ = 3.875
Ф = tan^-1(3.875) = 75.529°
Se cortan en punto (-28/31 , 66/31) y Forman un angulo de 75.529°
B) L1: Y=-3x+1 ; L2: -2y=3x+2
Y = -3X + 1: -2Y = 3X + 2 => Y = -3X/2 - 1
Y = Y
-3X + 1 = -3X/2 - 1
-3X + 3X/2 = - 1 - 1
-6X/2 + 3X/2 = -2
-3X/2 = -2
-3X = -4
X = -4/-3
X = 4/3
Reemplazo X en Y = -3X + 1
Y = -3(4/3) + 1 = -4 + 1
Y = -3
Punto de corte (4/3 , -3)
m1 = -3; m2 = -3/2
TanФ = [(m2 - m1)/(1 + m2m1)]
m2 - m1 = -3/2 - 3 = -3/2 - 6/2 = -9/2
m2m1 = (-3/2)(-3) = 9/2
1 + 9/2 = 2/2 + 9/2 = 11/2
TanФ = [(-9/2)/(11/2)]
Ф = tan^-1[-9/11] = -39.2894°
Se cortan en el punto (4/3 , - 3) y forman un angulo de -39.2894°
C)
L1: x+4 =y ; L2:-2x -5=y
Y = X + 4; Y = -2X - 5
Y = Y:
X + 4 = -2X - 5
X + 2X = -5 - 4
3X = -9
X = -3
Y = X + 4
Y = -3 + 4
Y = 1
Se cortan en el punto (-3 , 1)
m1 = 1; m2 = -2
TanФ = [(m2 - m1)/(1 + m2m1)]
m2 - m1 = -2 - 1 = -3
m2m1 = -2x1 = -2
1 - 2 = -1
TanФ = [(-3)/(-1)]
TanФ = 3
Ф = Tan^-1(39 = 71.5650°
Se cortan en el punto (-3 , 1) y forman un angulo de 71.5650°
D) L1: 2Y = -X + 4; L2: 3Y - 2X = 6
Y = -X/2 + 2; Y = 2X/3 + 2
Y = Y:
-X/2 + 2 = 2X/3 + 2
2 - 2 = 2X/3 + X/2
0 = 2X/3 + X/2
X = 0:
Y = -0/2 + 2
Y = 2
Se cortan en el punto (0 ,2)
m1 = -1/2; m2 = 2/3
TanФ = [(m2 - m1)/(1 + m2m1)]
m2 - m1 = 2/3 - (-1/2) = 2/3 + 1/2 = 7/6
m2m1 = (2/3)(-1/2) = -1/3
1 + (-1/3) = 1 - 1/3 = 2/3
TanФ = [(7/6)/(2/3)]
TanФ = [1.75]
Ф = Tan^-1(1.75)
Ф = 60.2551°
Se cortan el punto (0 , 2) y forman un angulo de 60.2551°