Question

3) Resolva os sistemas. DICA; resolva pelo método que você julgar mais conveniente!
a. x=-3+3y
x-y=1
b. x=1+y
x+y=10
c. x=2+y
x+y=7
.​

Answer 1

$\begin{cases}\mathsf{x=-3+3y}\\\mathsf{x-y=1}\end{cases}$

$\mathsf{x-y=1}\\\mathsf{-3+3y-y=1}\\\mathsf{2y=1+3}\\\mathsf{2y=4}\\\mathsf{y=\dfrac{4}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{y=2}}}}}\\\mathsf{x-2=1}\\\mathsf{x=1+2}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=3}}}}}$

$\dotfill$

$\begin{cases}\mathsf{x=1+y}\\\mathsf{x+y=10}\end{cases}$

$+\underline{\begin{cases}\mathsf{x-y=1}\\\mathsf{x+y=10}\end{cases}}$

$\mathsf{2x=11}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=\dfrac{11}{2}}}}}}\\\mathsf{\dfrac{11}{2}+y=10\cdot2}\\\mathsf{11+2y=20}\\\mathsf{2y=20-11}\\\mathsf{2y=9}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{y=\dfrac{9}{2}}}}}}$

$\dotfill$

c)

$\begin{cases}\mathsf{x=2+y}\\\mathsf{x+y=7}\end{cases}$

$+\underline{\begin{cases}\mathsf{x-y=2}\\\mathsf{x+y=7}\end{cases}}$

$\mathsf{2x=9}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=\dfrac{9}{2}}}}}}\\\mathsf{\dfrac{9}{2}+y=7\cdot2}\\\mathsf{9+2y=14}\\\mathsf{2y=14-9}\\\mathsf{2y=5}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{y=\dfrac{5}{2}}}}}}$

Answer 2

Oie, Td Bom?!

• Vou fazer pelo método de substituição.

a)

$\left\{\begin{matrix}</p><p> x = - 3 + 3y& \\ </p><p> x - y = 1& </p><p>\end{matrix}\right.$

• Substitua o valor dado de x na equação x - y = 1.

$- 3 + 3y - y = 1 \\ - 3 + 2y = 1 \\ 2y = 1 + 3 \\ 2y = 4 \\ y = \frac{4}{2} \\ y = 2$

• Substitua o valor dado de y na equação x = - 3 + 3 . 2.

$x = - 3 + 3 \: . \: 2 \\ x = - 3 + 6 \\ x = 3$

$S = \left \{(x \: , \: y) = (3 \: , \: 2) \right \}$

b)

$\left\{\begin{matrix}</p><p> x = 1 + y& \\ </p><p> x + y = 10& </p><p>\end{matrix}\right.$

• Substitua o valor dado de x na equação x + y = 10.

$1 + y + y = 10 \\ 1 + 2y = 10 \\ 2y = 10 - 1 \\ 2y = 9 \\ y = \frac{9}{2}$

• Substitua o valor dado de y na equação x = 1 + y.

$x = 1 + \frac{9}{2} \\ x = \frac{2 + 9}{2} \\ x = \frac{11}{2}$

$S = \left \{ (x \: , \: y) = ( \frac{11}{2} \: , \: \frac{9}{2} )\right \}$

c)

$\left\{\begin{matrix}</p><p> x = 2 + y& \\ </p><p> x + y = 7& </p><p>\end{matrix}\right.$

• Substitua o valor dado de x na equação x + y = 7.

$2 + y + y = 7 \\ 2 + 2y = 7 \\ 2y = 7 - 2 \\ 2y = 5 \\ y = \frac{5}{2}$

• Substitua o valor dado de y na equação x = 2 + y.

$x = 2 + \frac{5}{2} \\ x = \frac{4 + 5}{2} \\ x = \frac{9}{2}$

$S = \left \{(x \: , \: y) = ( \frac{9}{2} \: , \: \frac{5}{2}) \right \}$

Att. Makaveli1996