10 POINTS AND BRAINLIEST Please answer all 3 questions attached correctly.

Mathematics

1 answer:

lana66690 [7]3 years ago

5 0

Answer:

#1. Identity #2. 0 #3. No solution

Step-by-step explanation:

#1.

5y + 2 = (1/2)(10y+4)

5y + 2 = 5y + 2

This would be identity as the equation of the left and right are the same. This is not to be confused with no solution(explained below).

#2.

0.5b + 4 = 2(b+2)

0.5b + 4 = 2b + 4

0.5 b - 2b = 0

b = 0

#3.

-3x + 5 = -3x + 10

This equation has no solution because when you try to bring the -3x to one side, the x variable itself gets eliminated. So, how is it different from identity? Well in the first equation, it is true that when we try to bring the 5y one side it eliminates the y variable, however, that is also true for the constants(since if we try to bring the 2 to one side, it will be 2-2 which will equal 0, thus eliminating each other), but in this case, even if we remove the x, the constants will not equal 0, thus it will have no solution.

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Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?

skelet666 [1.2K]

The right answer is C)

Consistent and independent system of two linear equations is a system such that there is only one solution for the system, that is, the two straight lines cross at a point. So we can analyze each case and I have attached some graphs to provided you with examples. Those graphs aren't about the equations but it's about general cases:

A) Consistent and dependent. If we divide this given equation by 2 we get the same line. (See Figure 1)

B) Inconsistent. No solutions. (See Figure 2)

C) Consistent and Independent. (See Figure 3)

D) Consistent and dependent. If we multiply this equation by -1 we get the same line. (See Figure 1)