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Question 72622This question is from textbook Introductory and intermediate algebra
: use cramers rule to solve
2x = 7 + 3y
4x - 6y =3
This question is from textbook Introductory and intermediate algebra
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 2x = 7 + 3y
4x - 6y =3
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First arrange the two equations in the standard form of ax + by = c.
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The second (or bottom) equation is already in this form, but the first (or top) equation is
not. So we need to arrange the first equation into the standard form. We can do this by
subtracting 3y from both sides in the first equation to get 2x - 3y = 7.
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Now the two equations we are working with are:
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2x - 3y = 7 and
4x - 6y = 3
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Let's stop right here. Look at the left side of the equations. The left side of the second
equation is just double the left side of the first equation. The graphs of these two
equations are parallel lines with different points of intercept with the y axis. Recall that
for a common solution to exist the graphs must cross or at least have some point where they
touch. The graphs for these two equations are parallel lines and therefore they never intersect
each other. Therefore, this set of equations has no common solution and you might expect
that something unusual might happen to their determinants.
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The determinant formed by the coefficients of the x and y terms is:
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|+2 -3|
|+4 -6|
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[2*(-6)] - [(-3)*(+4)] = -12 - (-12) = -12 + 12 = 0
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There's what clues us in. If the determinant of the coefficients turns out to be zero
Cramer's rule cannot be applied because there isn't a common solution.
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Hope this straightens out your problem. If you worked the determinant and kept getting
zero, you were correct and this explanation tells you why that was happening.
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