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Solve system of equations and examine how many solutions have? x+i*y=-1 2x+3y=3i
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You may use substitution method, hence, you may use the first equation to express x in terms of y, such that:
`x = -1 - i*y`
Replacing `-1 - i*y` for `x` in the bottom equation, yields:
`2(-1 - i*y) + 3y = 3i`
`-2 - 2i*y + 3y = 3i`
You need to keep the terms that contain y to the left side, such that:
`y(-2i + 3) = 3i + 2 => y = (3i + 2)/(3 - 2i)`
`y = ((3i + 2)(3 + 2i))/((3 - 2i)(3 + 2i))`
`y = ((3i + 2)(3 + 2i))/(9 - 4i^2)`
Replacing `-1` for `i^2` yields:
`y = ((3i + 2)(3 + 2i))/13 => y = (9i + 6i^2 + 6 + 4i)/13`
`y = (9i -6 + 6 + 4i)/13`
`y = (13i)/13 => y = i`
Replacing `i` for `y` in equation `x = -1 - i*y` yields:
`x = -1 - i*i => x = -1 - i^2 => x = -1 + 1 => x = 0`
Hence, evaluating the solution to the system of equations, yields that the system has the unique solution `x = 0, y = i.`
Posted by sciencesolve on August 30, 2013 at 8:29 AM (Answer #1)
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