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2 years ago

Which of the following systems of equations has infinitely many solutions?

Mathematics

2 answers:

Sonja [21]2 years ago

3 0

Answer:

C. y = x + 4, 2y = 2x + 8

Step-by-step explanation:

The system has infinitely many solutions if the two equations are equivalent.

We can analyze the given systems to see:

2x + 7x + y = 6 ⇒ 9x + y = 6 ⇒ y = - 9x + 6
y = 9x + 6

Different slopes, there is one solution

y = 5x + 7
y = 2x + 8

Different slopes, there is one solution

y = x + 4
2y = 2x + 8 ⇒ y = x + 4

Same lines, infinitely many solutions

7x - y = 10 ⇒ y = 7x - 10
y = 6x + 8

Different slopes, there is one solution

Ainat [17]2 years ago

3 0

Solution:

When two equations are equivalent, it is infinitely many solutions because the two lines overlap each other.

Option A - 2x + 7x + y = 6 and y = 9x + 6

=> (9x + y = 6) = (y = 9x + 6)
=> (y = -9x + 6) ≠ (y = 9x + 6)

Option B - y = 5x + 7 and y = 2x + 8

=> (y = 5x + 7) ≠ (y = 2x + 8)

Option C - y = x + 4 and 2y = 2x + 8

=> (y = x + 4) = (2y = 2x + 8)
=> (y = x + 4) = (y = 2x/2 + 8/2)
=> (y = x + 4) = (y = x + 4)

Option D - 7x - y = 10 and y = 6x + 8

=> (7x - y = 10) = (y = 6x + 8)
=> (-y = -7x + 10) = (y = 6x + 8)
=> (y = 7x - 10) ≠ (y = -6x - 8)

Hence, Option C is correct.

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earnstyle [38]

Answer:

x=4.5,y=5,z=9

Step-by-step explanation:

First, we use the pythagorean theorem in the lower right triangle (with sides 4,x,6) and find x^2+4^2=6^2 and therefore x^2=6^2-4^2=20 so x=√20 which is approximately 4.5.

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2 years ago

8 Line in the xy-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the follo

iren2701 [21]

Answer:

The correct option is D.

Step-by-step explanation:

The slope of a line is the change in y with respect to x.

$m=\frac{y_2-y_1}{x_2-x_1}$

If the slope of a line is undefined it means it is a vertical line and a vertical line can not passes through three quadrants. So, option A is incorrect.

If the slope of a line is 0 it means it is a horizontal line and a horizontal line can not passes through three quadrants. So, option B is incorrect.

If the slope of a line is positive it means the value of y increases as x increases.

Since it is an increasing line, therefore after a certain period both x and y will positive. It means the line will passes through first quadrant. So, option C is incorrect.

If the slope of a line is negative it means the value of y decreases as x increases. It can passes through each of Quadrants II, III, and IV.

Therefore the correct option is D.