asked 87.9k views
1 vote
Find x and y in terms of a and b.
Sax + by = 0
x + y = 2
(x, y) =
(a + b)

1 Answer

4 votes
To solve for x and y, we can use substitution.

From the second equation, we have y = 2 - x.

Substituting this into the first equation, we get:

Sax + b(2 - x) = 0

Expanding this equation, we get:

Sax + 2b - bx = 0

Rearranging the terms, we get:

x(Sa - b) = 2b

Dividing both sides by (Sa - b), we get:

x = 2b/(Sa - b)

Substituting this value of x into the second equation, we get:

2b/(Sa - b) + y = 2

Substituting y = 2 - x, we get:

2b/(Sa - b) + (2 - 2b/(Sa - b)) = 2

Simplifying this equation, we get:

4b/(Sa - b) = 2

Multiplying both sides by (Sa - b)/2, we get:

2b = (Sa - b)

Simplifying this equation, we get:

b = a/2

Substituting this value of b into the equation for x, we get:

x = 2b/(Sa - b) = 2(a/2)/(Sa - a/2) = a/(2S - 1)

Substituting these values of x and y into the given point (x, y) = (a + b), we get:

(a/(2S - 1), 2 - a/(2S - 1)) = (a + a/2, a/2)

Therefore, the solution is:

x = a/(2S - 1) and y = 2 - a/(2S - 1).
answered
User AndrewBloom
by
8.1k points
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