Question

Rezolvati prin metoda substitutiei urmatoarele sisteme: c) {2x+3(y+x)-2y=-1 {3(x+y)-2y=1

Answer 1

Răspuns:

$\bf\red{\left \{ {{x=-1} \atop {y=4}} \right.}$

Explicație pas cu pas:

$\left \{ {{2x+3(y+x)-2y=-1} \atop {3(x+y)-2y=1}} \right. \iff2x+3y+3x-2y=-1\iff5+y=-1\\\iff x=-\frac{1}{5}-\frac{1}{5}y\iff 3(x+y)-2y=1\iff 3(-\frac{1}{5}-\frac{1}{5}y+y)-2y=1\\\iff 3(-\frac{1}{5}-\frac{4}{5}y)-2y=1\iff-\frac{3}{5}+\frac{12}{5}y-2y=1\iff-\frac{3}{5}+\frac{2}{5}y=1\\\iff-3+2y=5\iff2y=8\iff y=4$

$x=-\frac{1}{5}-\frac{1}{5}\times4\\x=-\frac{1}{5}-\frac{4}{5}\\x=-1$