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jeka57 [31]
3 years ago
10

1-Determine a solução dos sistemas abaixo pelo método de adição: a) {x + y = 5 {2x- y=9 b) {3x - y = 10 {x + y =18 Prfvr gente

Mathematics
1 answer:
xeze [42]3 years ago
5 0

a)

X + Y = 5

<u>2X - Y = 9     </u>  

X + 2X + Y - Y = 5 + 9

3X = 14

<h3>X = 14/3</h3>

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:

X+ Y = 5

14/3 + Y = 5

Y = 5 - 14/3

<h3>Y = 1/3</h3>

.........................

b)

3X - Y = 10

<u>X + Y = 18       </u>  

3X + X - Y + Y = 10 + 18

4X = 28

<h3>X = 7</h3>

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:

X + Y = 18

7 + Y = 18

Y = 18 - 7

<h3>Y = 11</h3>
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| x - 1 | = 5x + 10<br> Check for extraneous solutions.
Ronch [10]
[x-1]=5x+10

We have two equations:
1) x-1=5x+10

x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4

2) x-1=-(5x+10)

x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2

we have two  possible solutions:
solution₁;       x=-11/4
solution₂:       x=-3/2

we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4  - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4  + 10
[-15/4]=(-55+40) /4
15/4≠-15/4   This solution don´t work.

2) x=-3/2
[x-1]=5x+10
[-3/2  - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2  + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.

Therefore:

Answer: x=-3/2.
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