Question

Sa se rezolve sistemul de ecuatii
$2x - \frac{3y - 2}{5} egal \: 3 \\ 3y + \frac{2x + 3}{3} egal - \frac{4}{3}$

Answer 1

$\left\{\begin{matrix} 2x - \frac{3y - 2}{5} = 3 \: | \times 5& \\ \\ 3y + \frac{2x + 3}{3} = - \frac{4}{3} | \times 3 & \end{matrix}\right.$

$=\left\{\begin{matrix} 10x - 3y + 2 = 15 & \\ \\ 9y + 2x + 3 = - 4& \end{matrix}\right.$

$=\left\{\begin{matrix} 10x - 3y = 15 - 2 & \\ \\ 2x + 9y = - 4 - 3& \end{matrix}\right.$

$=\left\{\begin{matrix} 10x - 3y = 13 \: | \times 3& \\ \\ 2x + 9y = - 7& \end{matrix}\right.$

$=\left\{\begin{matrix} 30x - 9y = 39 & \\ \\ 2x + 9y = - 7 & \end{matrix}\right.$

$30x + 2x - 9y + 9y = 39 - 7$

$32x = 32 \: | \div 32$

$x = 1$

$2x + 9y = - 7$

$2 \times 1 + 9y = - 7$

$2 + 9y = - 7$

$9y = - 7 - 2$

$9y = - 9 \: | \div 9$

$y = - 1$

$S=\left\{(x,y)\right\}=\left\{(1,-1)\right\}$