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The functions are linearly dependent. Find constants, not all zero, such that?

User Colemik
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Final answer:

To find constants that make linearly dependent functions, we can rewrite the equations in the same form and solve for the variables. In this case, x = 1 and y = 2.

Step-by-step explanation:

Linearly dependent functions are functions that can be expressed as a linear combination of each other. In other words, one function can be written as a multiple of the other function.

In the given question, 7y = 6x + 8, 4y = 8, and y + 7 = 3x are all linear equations. To determine constants that make these functions linearly dependent, we can rewrite them in the same form. Let's start by rewriting the second equation as 4y = 8:

y = 8/4 = 2

Now that we have the value of y, we can substitute it into the other equations to find the values of x:

Substituting y = 2 in 7y = 6x + 8:
7(2) = 6x + 8
14 = 6x + 8
6x = 14 - 8 = 6
x = 6/6 = 1

Substituting y = 2 in y + 7 = 3x:
2 + 7 = 3x
9 = 3x
x = 9/3 = 3

Therefore, the constants that make these functions linearly dependent are x = 1 and y = 2.

User Elachell
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