Question

Resolva o sistema abaixo e determine os valores de x e y.
{x − y = 16x + y = 74

Answer 1

Resposta:

y=29

x=45

Explicação passo-a-passo:

x-y=16   x+y=74

x=16+y

x=16+29

16+y+y=74

2y=74-16

y=58/2   y=29

Answer 2

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$\boxed{\begin{array}{l}\begin{cases}\sf x-y=16\\\sf x+y=74\end{cases}\\\underline{\rm resoluc_{\!\!,}\tilde ao~pelo~m\acute etodo~de~Cramer:}\\\sf A=\begin{bmatrix}\sf1&\sf-1\\\sf1&\sf1\end{bmatrix}\\\sf det~A=1+1=2\\\sf A_x=\begin{bmatrix}\sf16&\sf-1\\\sf74&\sf1\end{bmatrix}\\\sf det~A_x=16+74=90\\\sf A_y=\begin{bmatrix}\sf1&\sf16\\\sf1&\sf74\end{bmatrix}\\\sf det~A_y=74-16=58\\\sf x=\dfrac{det~A_x}{det~A}=\dfrac{90}{2}=45\\\sf y=\dfrac{det~A_y}{det~A}=\dfrac{58}{2}=29\\\sf S=\{45,29\}\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf x-y=16\\\sf x+y=74\end{cases}\\\underline{\rm resoluc_{\!\!,}\tilde ao~pelo~m\acute etodo~da~comparac_{\!\!,}\tilde ao\!:}\\\begin{cases}\sf y=x-16\\\sf y=74-x\end{cases}\\\sf x-16=74-x\\\sf x+x=74+16\\\sf 2x=90\\\sf x=\dfrac{90}{2}\\\sf x=45\\\sf y=x-16\\\sf y=45-16\\\sf y=29\\\sf S=\{45,29\}\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf x-y=16\\\sf x+y=74\end{cases}\\\underline{\rm resoluc_{\!\!,}\tilde ao~pelo~m\acute etodo~da~substituic_{\!\!,}\tilde ao\!:}\\\begin{cases}\sf y=x-16\\\sf x+y=74\end{cases}\\\sf x+x-16=74\\\sf 2x=74+16\\\sf 2x=90\\\sf x=\dfrac{90}{2}\\\sf x=45\\\sf y=x-16\\\sf y=45-16\\\sf y=29\\\sf S=\{45,29\}\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf x-y=16\\\sf x+y=74\end{cases}\\\underline{\rm resoluc_{\!\!,}\tilde ao~pelo~m\acute etodo~da~adic_{\!\!,}\tilde ao\!:}\\+\underline{\begin{cases}\sf x-\backslash\!\!\!y=16\\\sf x+\backslash\!\!\!y=74\end{cases}}\\\sf 2x=90\\\sf x=\dfrac{90}{2}\\\sf x=45\\\sf x-y=16\\\sf 45-y=16\\\sf y=45-16\\\sf y=29\\\sf S=\{45,29\}\end{array}}$