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NARA [144]
2 years ago
15

The linear combination method is applied to a system of equations as shown.

Mathematics
1 answer:
Kay [80]2 years ago
4 0

Answer:

hi

Step-by-step explanation:

Option 4th is correct

The solution of the system of equations is, (9, 3)

Step-by-step explanation:

Given the system of equations:

⇒                .....[1]

           

⇒                 .....[2]

Add equation [1] and [2] we have;

Divide both sides by 2 we have;

Substitute x = 9 in [1] we have;

Subtract 9 from both sides we have;

2y = 6

Divide both sides by 2, we have;

y = 3

Therefore, the solution of the system of equations is, (9, 3)

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Describe the following variation: y/x2=5
Firdavs [7]
We are asked to describe the variation \displaystyle{ \frac{y}{x^2}=5, 

that is y=5x^2

for x≠0, in which case x=y=0, we distinguish the following intervals:

I   = (-infinity, -1]
II  = (-1, 0)
III = (0, 1)
III = [1, infinity)

Case I, consider the cases (examples)   x= -5, and x= -6

5(-6)^2\ \textgreater \ 5(-5)^2, so we can conclude that the greater the x, the smaller the y.

Case II, consider x= -1/2 < x=-1/3

5(-\frac{1}{2})^2= \frac{5}{4}\\\\ 5(-\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \  \frac{5}{4}

thus, the greater the x, the smaller the y.


Case III, consider the cases (examples)   x= 5, and x= 6

5(6)^2\ \textgreater \ 5(5)^2, so we can conclude that the greater the x, the greater the y.

Case III, consider x= 1/3 < x=1/2

5(\frac{1}{2})^2= \frac{5}{4}\\\\ 5(\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \ \frac{5}{4}

thus, the greater the x, the greater the y.


Conclusion:

y=0 only if x is 0. Otherwise y>0 always:

for x<0,   x and y are inversely proportional

for x>0,   x and y are directly proportional.


Remark, an other possible consideration in cases could be x<0 and x>0 only.


Remark, 
another approach is considering the graph of y=5x^2, which is a parabola, with the vertex at (0, 0) opening upwards.

From the graph we can find the same conclusion. That is we can see that the farer we get away from the y-axis, in both direction, the larger the values of y become.

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Answer:

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