Algebra Know-It-ALL
Subtracting 15 from each side gives us − 10 r+ 5 s=− 15 When we add 10r to each side, we get 5 s= 10 r− 15 Finally, we can divid ...
646 Worked-Out Solutions to Exercises: Chapters 11 to 19 and y= (−2/3)x− 2 There’s no morphing for us to do. So let’s go ahead a ...
by moving to the right by Δy= 4 units and upward by Δx= 3 units. The slope is therefore m=Δx/Δy = 3/4 Remember that the slope of ...
648 Worked-Out Solutions to Exercises: Chapters 11 to 19 Now that we know the slope and the x-intercept for line M*, we can writ ...
the range is the entire set of real numbers. That means there is more than one value in the range for the single value in the do ...
650 Worked-Out Solutions to Exercises: Chapters 11 to 19 Now let’s switch the left and right sides of the equation to get mx=y−b ...
The second and third revised equations we obtained in the section “Eliminate One Variable” were 2 x− 5 y−z=− 1 and 3 x+ 6 y− 7 ...
652 Worked-Out Solutions to Exercises: Chapters 11 to 19 and y=−18/223 These are the same solutions we obtained in the chapter t ...
To use the morph-and-mix method, we must get the equations into SI form. We’re told to treat x as the dependent variable, so we ...
654 Worked-Out Solutions to Exercises: Chapters 11 to 19 For reference, here again is the second equation stated in Prob. 1: 2 ...
Check! Finally the fourth: y= 4 x+ 1 1 = 4 × 0 + 1 1 = 0 + 1 1 = 1 We can now be confident that the solution to the system is in ...
656 Worked-Out Solutions to Exercises: Chapters 11 to 19 We morph the first equation as follows: x=y−z− 7 x−y=−z− 7 x−y+z=− 7 Ne ...
Here are the equations, derived directly from the coefficients in the matrix: 0 x+ 4 y+ (−z)=− 2 5 x+ (−3/2)y+ 8 z= 1 x+y+z= 1 H ...
658 Worked-Out Solutions to Exercises: Chapters 11 to 19 Now let’s multiply the second row by 13 and the third row by 4. That gi ...
We need to turn the 9,152 in the first row into 0. We’ll have to work with the third row to make it happen. Suppose 9,152 divide ...
660 Worked-Out Solutions to Exercises: Chapters 11 to 19 Here are the equations from solution to Prob. 3, which we hope we have ...
These equations are all in ideal form for conversion to the matrix 1111 1112 1113 Now let’s try to get this into unit diagonal f ...
662 Worked-Out Solutions to Exercises: Chapters 11 to 19 effect, says that 0 is equal to some nonzero real number. That’s absurd ...
These worked-out solutions do not necessarily represent the only way a problem can be fig- ured out. If you think you can solve ...
j−^6 = 1/(j^6 ) = 1/(−1) =− 1 j−^8 = 1/(j^8 ) = 1/1 = 1 ↓ and so on, forever To solve this problem, we need a little intuition. ...
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