Question

Determine os pontos em comum entre cada par de retas:
A) y = 3 x + 1 e y = 2 x - 5
B) y = 4 x + 3 e y = 5 x - 2
C) y = x + 3 e y = 9 - x
D) y = x + 3 / 2 e y = x - 2 / 6

Answer 1

Bom, vamos lá:

a)

$\left \{ {{y=3x+1} \atop {y=2x-5}} \right.$

$3x+1 = 2x - 5 \\ x = -6 \\ \\ y = 3x + 1 \\ y = 3*(-6) + 1 \\ y = -18 + 1 \\ y = -17 \\ \\ P(-6,-17)$

b)

$\left \{ {{y=4x+3} \atop {y=5x-2}} \right.$

$4x + 3 = 5x - 2 \\ 3 + 2 = 5x - 4x \\ x = 5 \\ \\ y = 4x + 3 \\ y = 4*(5) + 3 \\ y = 20 + 3 \\ y = 23 \\ \\ P(5,23)$

c)

$\left \{ {{y=x+3} \atop {y=9-x}} \right.$

$x + 3 = 9 - x \\ 2x = 6 \\ x = 3 \\ \\ y = x + 3 \\ y = 3+ 3 \\ y =6 \\ \\ P(3,6)$

d)

$\left \{ {{y= \frac{x+3}{2} } \atop {y= \frac{x-2}{6} }} \right.$

$\frac{x+3}{2} = \frac{x-2}{6} \\ \\ 6(x+3) = 2(x-2) \\ 6x + 18 = 2x - 4 \\ 4x = -22 \\ x = - \frac{11}{2} \\ \\ y = \frac{x+3}{2} \\ \\ y = \frac{- \frac{11}{2}+3}{2} \\ \\ y = -\frac{5}{2} * \frac{1}{2} \\ \\ y = -\frac{5}{4}$