Question

as retas de equação 4x-3y+5=0 e 5x-y+9=0 se interceptam em um ponto. Dê as coordenadas desse ponto de intersecção das retas.

Answer 1

$\left\{\begin{array}{ccc}4x-3y+5 = 0\\5x-y+9 = 0\\\end{array}\right \to \left\{\begin{array}{ccc}4x-3y=-5\\5x-y=-9\\\end{array}\right \to \left\{\begin{array}{ccc}4x-3y=-5\\15x-3y=-27\\\end{array}\right \\ \\ \\ \to 19x = -32 \\ \\ \boxed{x = \frac{-32}{19} } \\ \\ 4*( \frac{-32}{19})-3y = -5 \\ \\ \frac{-128}{19}-3y = -5 \\ \\ \frac{-128}{19} = -5+3y \\ \\ -128 = -95+57y \\ \\ 57y = -33 \\ \\\boxed{ y = \frac{-33}{57} = \frac{-11}{19} } \\ \\ S = \{ \frac{-32}{19},\frac{-11}{19}\}$

Espero ter ajudado. :))