A. Letters and Lengths
B. Solving Linear Eq'ns - WS
C. Solving Linear Eq'ns - No Sticks
D. Almost One
E Substitution Methods
F. Two More Methods
G. Larger Systems
H.  Exercises to Try

Read them in order

(i) x + 20 = 29 WS
(ii) 2x + 6 = 24 WS
(iii) 3x + 10 = 32 WS
(iv) 5a + 16 = 3a+ 24 WS
(v)  (½)x + 8 = 24½ WS
(vi)  (¾)a + 16 = (¼)a+ 24 WS
(vii) (¾)q + 17 = 32 WS
(viii) 13 =[2/3]x +7 twice WS
(5/6)q + 8+(5/6) = 14 + (2/3) WS
Proper Use of Equal Sign

Up
A. Letters and Lengths
B. Solving Linear Eq'ns - WS
C. Solving Linear Eq'ns - No Sticks
D. Almost One
E Substitution Methods
F. Two More Methods
G. Larger Systems
H.  Exercises to Try
 

Exercises

Instruction:  If your method is correct, but your check says your answer is wrong, writes OOPs besides your check, and go on. Correct your work later. The error will be somewhere between the start of your solution and the end of the check.

1A. (4 points) Express A and B as simplified, improper fraction:  For the calculation of A, cancel common factors in numerators and denominators before multiplication. For the calculation of B, use the least common denominator.

A =

25 27

.

81 100

B =

3 26

+

7 10

For A and B, there is 1 point for right answer and 4 points for following instruction on how to arrive at the answer. Show work!  If you use a calculator (not recommended), show the reasoning needed to arrive at your solution without its use.

2 . (6 points) Express as a single, simplified, improper fraction:

A= [

5 4

¸

35 24

] ¸

2 7

B=

4 5

[

5 4

+

35 24

+

2 7

]

C =

8 15

[

25 4

+

75 8

+

15 2

]

3A.   (4 points) Solve the (scrambled) triangular system

3x +  2y +  z = 65
      3y      = 45
6x +   y      = 75

3B.  (4 points) Solve the (scrambled) triangular system

2x +  3y + 4z = 21
      8y + 2z = 26
      5y      = 15

 4. (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.

5.  (a)   (8 points)  Solve for x and y  - obtain a literal solution.

 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

6. (12 points)  Solve 

3x + 2y = 17
2x -  y =  2

7. (10 points)  Solve  

  x - 2y = 4
-3x +  y = 3

8.  (12 points)  Solve  

 x +  y +  z= 12
2x + 3y + 5z = 32
6x + 7y +  z =64

9.  (10 points)  Solve  - note minus sign in each equation.

 -x +  y +  z = 10 
   x  - y +  z = 8
   x +  y -  z = 6
 x +  y +  z - w =14

10.  (4 points)  (i)   Show by substitution that the formulas

x =

dg ad-bc

and  y =

-cg ad-bc

          satisfy (solve) the system

 ax + by = g
 cx + dy = 0

     (2 points) (ii)  Give values  for coefficients a, b, c, d, and g  to make the system in (i) the same as 

 4x + y  = 10
  x + 4y = 0

  (4 points) (iii) Use the formulas in (i) to solve the system in (ii)

 [ Back ] [ Up ] [Top of this Page]  
Have you  been to the Site Entrance: www.whyslopes.com?

Road Safety Message  Do not walk on a road with your back to the traffic - rule of thumb
Please report by email,  errors in mathematics or grammar or terminology to site author
If a mathematics topic you need is not covered in site pages,  report that as well. Topics in most demand
will be covered first in site growth.  

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby,  All Rights Reserved.