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Question 72620This question is from textbook Introductory and intermediate algebra
: solve this system of equations. if it is unsolvable say so.
3x + 4y + 5z=8
1x - 2y + 3z= -6
2x - 4y + 6z=8
This question is from textbook Introductory and intermediate algebra
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Unsolvable.
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In order to be a solvable system for three variables, all three equations must be independent.
But look at the left sides of equations two and three. If you multiply both sides of the
second equation by 2 you get:
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2x - 4y + 6z = -12
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Notice that the left side of this equation is identical to the left side of equation 3.
That indicates that the graph of the line represented by equation two is parallel to the
graph of the line represented by equation 3. Since they are parallel lines they never
intersect at a common point, so they can't have a common solution.
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If you are familiar with Cramer's rule you can calculate the determinant of the coefficients
on the left side of these 3 equations, and the determinant equals zero. This also
indicates that there is no common solution for these three equations.
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Hope this explanation helps you to understand why you can say the equations have no common
solution just by inspecting them.
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