Question

Resolva o sistema abaixo:

Answer 1

a)

{x+y=3

+{x–y=1

$x + x = 3 + 1 \\ 2x = 4 \\ x = \frac{4}{2} \\ x = 2$

$x + y = 3 \\2 + y = 3 \\ y = 3 - 2 \\ y = 1$

S={2,1}

b) {2x+y=–1 ×(-2)

{x+2y=1

{–4x–2y=2

{x+2y=1

$- 4x + x = 2 + 1 \\ - 3x = 3 \times ( - 1) \\ 3x = - 3 \\ x = - \frac{3}{3} \\ x = - 1$

$x + 2y = 1 \\ - 1 + 2y = 1 \\ 2y = 1 + 1 \\ 2y = 2 \\ y = \frac{2}{2}$

$y = 1$

S={–1,1}

c)

{x+4y=4

{x–y=4×4

{x+4y=4

{4x–4y=16

$x + 4x = 4 + 16 \\ 5x = 20 \\ x = \frac{20}{5} \\ x = 4$

$x - y = 4 \\ y = x - 4 \\ y = 4 - 4 \\ y = 0$

S={4,0}

d)

{2x+y=5

{x+y=1×(–1)

{2x+y=5

{–x–y=–1

$2x - x = 5 - 1 \\ x = 4$

$x + y = 1 \\ 4 + y = 1 \\ y = 1 - 4 \\ y = - 3$

S={4–3}