If g + 3f - 1 = 0 and 7f + 3g - 7 = 0 intersect at coordinate (f, g) in the fg-plane, what is the value of g?(A) -2(B) 1(C) 3(D) 5(E) 7

Question

If `g + 3f - 1 = 0` and `7f + 3g - 7 = 0` intersect at coordinate `(f, g)` in the fg-plane, what is the value of `g`?

(A) -2
(B) 1
(C) 3
(D) 5
(E) 7

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Solution

To find the value of g, we can solve the system of equations given by:

g + 3f - 1 = 0 ...(1) 7f + 3g - 7 = 0 ...(2)

First, we can rearrange equation (1) to solve for g:

g = 1 - 3f ...(3)

Then, we substitute equation (3) into equation (2):

7f + 3(1 - 3f) - 7 = 0 7f + 3 - 9f - 7 = 0 -2f - 4 = 0 -2f = 4 f = -2

Substitute f = -2 into equation (3):

g = 1 - 3(-2) g = 1 + 6 g = 7

So, the value of g is 7 (E).

This problem has been solved

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