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Inconsistent systems example
Example Solve the given systems of equations.
x - y = 6
-2x + 2 y = 1
Solution
We can utilize either method here, although it looks like substitution would possibly be slightly easier.
We'll solve out the first equation for x & substitute that in the second equation.
x = 6 + y
-2 (6 + y )+ 2 y = 1
-12 - 2 y + 2 y = 1
-12 =1 ??
Thus, this is clearly not true and there doesn't seem to be a mistake anywhere in our work. Hence, what's the problem? To see let's graph these two lines and illustrates what we get.
It seem that these two lines are parallel (can you check that with the slopes?) and we know that two parallel lines along with different y-intercepts (that's significant) will never cross.
Since we saw in the opening discussion of this section solutions revel the point where two lines intersect. If two lines don't intersect we can't comprise a solution.
Thus, when we get this kind of nonsensical answer from our work we contain two parallel lines and there is no solution to this system of equations.
This system is called inconsistent. Note that if we'd utilized elimination on this system we would have ended up with a similar nonsensical answer.
Miscellaneous Functions The importance of this section is to introduce you with some other functions that don't really need the work to graph that the ones which we've looked
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s-1.75=0.02
what is 2+2?
#7.
Consider the linear transformation (a) Find the image of (3 , -2 , 3) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the trans
y = 4 - 3x /1 + 8x for x. Solution This one is very alike to the previous instance. Here is the work for this problem. y + 8xy = 4 - 3x 8xy + 3x = 4 - y X(8 y +3)
(734)base 8=()base16
Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition. Given two functions
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