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YOU are better than YOU think. Show yourself how: |
-/[]\- Logic
Mastery Do not leave here without it - Logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. |
-/[]\- After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6; For online automated help in senior high school maths & calculus, visit quickmath.com For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com With overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck. |
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Explore collaborative whiteboards from groupboard, twiddla or scriblink. |
Problems on Solving Linear Equations
Instruction: When solving linear equations, show all work and show
the calculations that check or test your solution. Suggestion:
If your method is correct, but your check says your answer is wrong, writes OOPs
besides your check, and go on. Correct your solution later.
1. (12 points) Solve the (scrambled) triangular system
3
x + 2y + z = 65
3y = 45
6x + y = 75
Do not use elimination.
2. (12 points) Solve by Gaussian Elimination
3x + 2y = 17
2x - y = 2
3. (12 points) Solve by Gaussian Elimination
x + y + z= 12
2x + 3y + 5z = 32
6x + 7y + z =64
3. (a) (8 points) Solve for x and y
ax = p
bx + cy = q
(b) (2 points) Verify (check) your solution.
(c)(2 points) Use your formulas for the solution in (a) to
solve
4x = 10
2x + 2y = 8
4. (2 points) Suppose w = x + y + z + 12 and x+y+z= 20. Find the
value of w.
5. (Bonus 4 points) Find w in terms of x if w = 4z+3, z = 3(y + 2) and y = x-2.
6. (Bonus 2 points) John has twice as many apples as Harry. Harry
and John together have 18 apples. Introduce notation for the number of
apples each has. Write down a system of two equations in two unknowns that would
allow you to find the number of apples each has. Do not solve the system.
7. (Bonus 2 points) In arithmetic with real numbers, the product AB of
two real numbers A and B is always nonzero when both factors A and B are
nonzero. What can you say for certain about two real numbers A and B
if their product AB =0 ?
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Algebra, Odds & Ends,
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Study With Others:
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In Volume 2, Three Skills for Algebra, Chapters 8 to 14 and postscript What is a Variable point to a greater & clear use of words in algebra. Chapter 14 introduces a 4th skill for algebra, an elaboration of the third: - The direct and indirect use of formulas, numerically and algebraically, is unifying theme that should be mentioned aloud, with words, in each and every use of formula.