Question

sabendo que os pares x1y1 e x2y2 são as soluções do sistema {y=3-x x²+y(4-x)=7 determine o valor de a)x1+x2 b)y1+y2

Answer 1

(1) $y=3-x$
(2) $x^2+y(4-x)=7$

(3)  1 ---> 2
$x^2+(3-x)(4-x)=7\\ 2x^2-7x+12=7\\ 2x^2-7x+5=0\\ (2x-5)(x-1)=0\\ \\ x\in\left\{1,\dfrac{5}{2}\right\}$

De la ecuación (1) se deduce

$(x,y)\in\left\{(1,2);\left(\dfrac{5}{2},\dfrac{1}{2}\right)\right\}\\ \\ \\ \boxed{x_1+x_2 = \dfrac{7}{2}}\\ \\\\ \boxed{y_1+y_2=\dfrac{5}{2}}$