Question

x-y=1
2x+y=5
mx-ny=-1
nx+my=2

Calcular m e n de modo que sejam equivalentes os sistemas

Answer 1

$\left \{ {{I. x-y=1} \atop {II. 2x+y=5}} \right.$
I. x=1+y
II. 2.(1+y) + y = 5
    2 + 2.y + y = 5
    3.y = 5 - 2
    3.y = 3
    y = 3/3
    y= 1
II. 2.x + 1 = 5
    2.x = 5 - 1
    x = 4/2
    x = 2

$\left \{ {{mx-ny=-1} \atop {nx+my=2}} \right.$
$\left \{ {{I. 2.m - 1.n=-1} \atop {II. 2.n+1.m=2}} \right.$
I. 2m - 1n = -1
   -n = -1 - 2.m
   n = +1 + 2m
II. 2.(1 + 2m) + m = 2
    2 + 4m + m = 2
    5m = 2 - 2
    m = 0/5
    m = 0
II. 2n + 0 = 2
    2n = 2
    n = 2/2
    n = 1


n = 1
m = 0
x = 2
y = 1