What is the value of b in the solution to the system of equations below?3a - b = 18a + 3b = -4a)-10b)-3c)3d)6e)cannot be determined with the given informationCorrect answer is option 'B'. Can you explain this answer?

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What is the value of b in the solution to the system of equations below?
3a - b = 18
a + 3b = -4

a)
-10
b)
-3
c)
3
d)
6
e)
cannot be determined with the given information

Correct answer is option 'B'. Can you explain this answer?

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What is the value of b in the solution to the system of equations belo...

To solve this problem, add the two equations, or multiples of them, so that cancellation occurs and you can solve for the b variable. If the equation a + 3b = -4 is multiplied by -3, the result is -3a - 9b = 12. The addition of -3a - 9b = 12 to the second equation is shown below:
3a - b = 18
-3a - 9b = 12
-10b = 30
By canceling out the a terms, you can solve for b:
b = 30/-10 = -3.

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Most Upvoted Answer

What is the value of b in the solution to the system of equations belo...

To find the value of b in the given system of equations, we can use the method of substitution or elimination.

1. Method of Substitution:
We are given the following system of equations:
3a - b = 18 ...(1)
3b = -4a ...(2)

From equation (2), we can rearrange it to get:
4a + 3b = 0 ...(3)

Now, we can solve equations (1) and (3) simultaneously to find the value of b.

From equation (1), we can isolate b:
b = 3a - 18

Substituting this value of b into equation (3), we get:
4a + 3(3a - 18) = 0
4a + 9a - 54 = 0
13a = 54
a = 54/13

Now, substituting the value of a back into equation (1), we can find the value of b:
3(54/13) - b = 18
162/13 - b = 18
- b = 18 - 162/13
- b = (234 - 162)/13
- b = 72/13

Therefore, the value of b is -72/13.

2. Method of Elimination:
We are given the following system of equations:
3a - b = 18 ...(1)
3b = -4a ...(2)

We can multiply equation (2) by 3 to make the coefficients of b the same:
9b = -12a ...(4)

Now, we can add equations (1) and (4) to eliminate b and solve for a:
3a - b + 9b = 18 - 12a
3a + 8b = 18 - 12a
15a = 18
a = 18/15
a = 6/5

Substituting the value of a back into equation (1), we can find the value of b:
3(6/5) - b = 18
18/5 - b = 18
- b = 18 - 18/5
- b = (90 - 18)/5
- b = 72/5

Therefore, the value of b is -72/5.

However, none of the given answer choices match -72/5. Therefore, the correct answer is that the value of b cannot be determined with the given information.

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What is the value of b in the solution to the system of equations below?3a - b = 18a + 3b = -4a)-10b)-3c)3d)6e)cannot be determined with the given informationCorrect answer is option 'B'. Can you explain this answer?

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