Question

4-Usando o método da substituição calcule a solução dos sistemas abaixo: a) { x=3y x+ 4y=14. b) {x-y =2 2x + y = 22.​

Answer 1

Resposta:

A)(x,y) = $\left[\begin{array}{ccc}\\14,\frac{7}{23} \\\end{array}\right]$ B)(x, y) = ($\frac{44}{23}$ , - $\frac{462}{23}$)

Explicação passo a passo:

A)$\left \{ {{x=4} \atop {3yx+4y=14}} \right.$

3y × 14 + 4y = 14

y = $\frac{7}{23}$

(x,y) = $\left[\begin{array}{ccc}\\14,\frac{7}{23} \\\end{array}\right]$

14=3 × $\frac{7}{23}$ × 14 × 4 × $\frac{7}{23}$ = 14

14 = 14 =14

(x,y) = $\left[\begin{array}{ccc}\\14,\frac{7}{23} \\\end{array}\right]$

B)$\left \{ {{x-y=22} \atop {22x+y=22}} \right.$

23x = 44

x = $\frac{44}{23}$

$\frac{44}{23}$ - y = 22

y= - $\frac{462}{23}$

(x, y) = ($\frac{44}{23}$ , - $\frac{462}{23}$)

$\frac{44}{23}$ - (- $\frac{462}{23}$) = 22 × $\frac{44}{23}$ + (- $\frac{462}{23}$) = 22

22 = 22 = 22

(x, y) = ($\frac{44}{23}$ , - $\frac{462}{23}$)