Question

Решить систему уравнений
2u + v = 7
{
|u - v| = 2

Answer 1

$\ left { {{2u+v=7} atop {|u-v|}=2}} right. \ \ left { {{v=7-2u} atop {|u-(7-2u)|}=2}} right. \ left { {{v=7-2u} atop {|u-7+2u|}=2}} right. \ left { {{v=7-2u} atop {|3u-7|}=2}} right. \ \ |3u-7|}=2 \ \ 3u-7=2 \ 3u=2+7 \ 3u=9 \ u= frac{9}{3} \ u=3 \ \ 3u-7=-2 \ 3u=-2+7 \ 3u=5 \ u= frac{5}{3} \ u=1 frac{2}{3} \ u approx1.(6)$

$begin{cases}v=7-2u\ u_1=3\ u_2= frac{5}{3}end{cases} \ begin{cases}v_1=7-2*3\ v_2=7-2* frac{5}{3} \ u_1=3\ u_2= frac{5}{3}end{cases} \ begin{cases}v_1=7-6\ v_2=7- frac{10}{3} \ u_1=3\ u_2= frac{5}{3}end{cases} \ begin{cases}v_1=1\ v_2=6 frac{3}{3} - 3frac{1}{3} \ u_1=3\ u_2= frac{5}{3}end{cases} \ begin{cases}v_1=1\ v_2=3 frac{2}{3} } \ u_1=3\ u_2=1 frac{2}{3}end{cases} \ begin{cases}v_1=1\ v_2=3 ,(6) \ u_1=3\ u_2=1 ,(6)end{cases}$


Ответ: v=1 u=3; v=3.(6) u=1.(6)