Question

Aplicando as propriedades da soma e da diferença, calcule os valores de x e y, y é diferente de 0.
$\frac{x }{y} = \frac{2}{3} \\ x + y = 20$
e
$\frac{x}{y} = \frac{5}{3} \\ x - y = 40$

Answer 1

x......2.........x = 2
_..=.._..=> ........._..y
y......3.................3

x + y = 20

Substiruindo

x + y = 20

2/3 y + y = 20

2/3 y + 3y/3 = 20

6y/3 = 20

6y = 20 * 3

6y = 60

y = 60/6

y = 10


Substituindo " y = 10 "

x = 2
......._..y
.......3

x = 2(10)
......._
.......3

x = 20
.......__
.........3

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x ....5.........x = 5
_..=.._..=>........._..y
y.......3...............3

x - y = 40

Subastituindo

x - y = 40

5y/3 - y = 40

5y/3 - 3y/3 = 40

2y/3 = 40

2y = 40 *3

2y = 120

y = 120/2

y = 60


Substituindo " y = 60 "

x = 5
......._..y
.......3

x = 5 * (60
......._
.......3

x = 300
......____
.........3

x = 100