Question

sistem de ecuație prin metode substituției
2(x+y-1)+3(x-y+2)=15
5(x-y-1)+2(x-y+4)=-4
urgeeent

Answer 1

$\left\{\begin{matrix} 2(x + y - 1) + 3(x - y + 2) = 15\\ 5(x - y - 1) + 2(x - y + 4) = - 4\end{matrix}\right.$

$\left\{\begin{matrix} 2x + 2y - 2 + 3x + 3y + 6 = 15\\ 5x - 5y - 5 + 2x - 2y + 8 = - 4\end{matrix}\right.$

$\left\{\begin{matrix} 5x + 5y + 4 = 15\\ 8x - 7y + 3 = - 4\end{matrix}\right.$

$\left\{\begin{matrix} 5x + 5y = 15 - 4\\ 8x - 7y = - 4 - 3\end{matrix}\right.$

$\left\{\begin{matrix} 5x + 5y = 11\\ 8x - 7y = - 7\end{matrix}\right.$

$x = \frac{11 - 5y}{5}$

$8x - 7y = - 7$

$8 \times \frac{11 - 5y}{5} - 7y = - 7$

$\frac{88 - 40y}{5} - 7y = - 7 \: | \times 5$

$88 - 40y - 35y= - 35$

$- 40y - 35y = - 35 - 88$

$- 75y = - 123 \: | \times ( - 1)$

$75y = 123$

$y = \frac{123}{75}$

$y = 1.64$

$5x + 5y = 11$

$5x + 5 \times 1.64 = 11$

$5x + 8.2 = 11$

$5x = 11 - 8.2$

$5x = 2.8$

$x = \frac{2.8}{5}$

$x = 0.56$