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MTH-4101-2 B
                              Equations & Inequalities II

1. Without calculating, what is the solution of the system of equations below?
                                            y




                                                                       x




                                                                                      /5

2. Without calculating, determine the solution of the system of equations below:

           1)   x + −=
                   y 3 0
                                                            2)   2 x −−
                                                                      y 9 =0




                x        y                              x         y
                0         3                             0         -9
                1         2                             1         -7
                2         1                             2         -5
                3         0                             3         -3
                4        -1                             4         -1
                5        -2                             5          1
                6        -3                             6          3




           ANS: ___________________________________

                                                                                      /3

3. Without calculating, express as a system of equations of the first degree in two
   variables.

   Nick is twice Richard’s age. If the difference between their ages is 30, what is the
   age of each man?




                                                                                      /5
4. Solve graphically the system of equations. Set up tables of values, identify the
   type of lines and determine the solution set.
                                                          y
       1)    2 x −−
                  y 8 =0




       2)    −−
              x 1 =2y




                                                                                  x




                                                                                      /5



5. Solve graphically the system of equations. Set up tables of values, identify the
   type of lines and determine the solution set.
                            y
                                                              1)   − +=
                                                                    2y x 0




                                                              2)   3x − =
                                                                      4y −
                                                                         8




                                                    x




                                                                                      /5
6. Solve each system of equations by a method of your choice:

   a) 1)    2x −3y =7




       2)   − + =( y +
             x 2 9   1)




                                                                /10

   b) 1)    y +2x =31




       2)   2 y −=
                 x 12




                                                                /10

   c) 1)    2y + =
                x 0




            3   5
       2)   4
              x+ =y
                2




                                                                /10
7. Jack and Isabelle had a combined amount of $210. Jack spent one-third of what
   he had, and Isabelle one-fifth. The sum of the expenses totaled $64. How much
   did each of them start out with?




                                                                                        /9

8. Cut 25 into two parts, such that the sum of six times one part and eight times the
   other part is 170. What are the values of the two parts?




                                                                                        /9

9. Find two numbers whose difference is 20 and one third of their sum is 40.




                                                                                        /9
Given the system of inequalities represented below:
                                                               y




       1)      x + ≤
                  y 2




       2)      − +≥
               2x y −
                    4




                                                                                         x




   State whether or not the given ordered pairs are solution-pairs of the system.

   Answer by yes or no.

   a) (0, 0)     ______________

   b) (4, 1)     ______________

   c) (–1, 1) ______________

   d) (0, –2) ______________

                                                                                    /4

10. Draw the graph representing the solution set of the following system of
    inequalities:
                                                      y
       1) y + x ≤ 3

       2) y – 2x ≥ –3




                                                                               x




                                                                                    /8
11. Draw the graph representing the solution set of the following system of
    inequalities:
                           y
                                                       1) y – 2x ≥ 4

                                                       2)   y <2




                                                   x




                                                                              /8

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Mth 4101-2 b

  • 1. MTH-4101-2 B Equations & Inequalities II 1. Without calculating, what is the solution of the system of equations below? y x /5 2. Without calculating, determine the solution of the system of equations below: 1) x + −= y 3 0 2) 2 x −− y 9 =0 x y x y 0 3 0 -9 1 2 1 -7 2 1 2 -5 3 0 3 -3 4 -1 4 -1 5 -2 5 1 6 -3 6 3 ANS: ___________________________________ /3 3. Without calculating, express as a system of equations of the first degree in two variables. Nick is twice Richard’s age. If the difference between their ages is 30, what is the age of each man? /5
  • 2. 4. Solve graphically the system of equations. Set up tables of values, identify the type of lines and determine the solution set. y 1) 2 x −− y 8 =0 2) −− x 1 =2y x /5 5. Solve graphically the system of equations. Set up tables of values, identify the type of lines and determine the solution set. y 1) − += 2y x 0 2) 3x − = 4y − 8 x /5
  • 3. 6. Solve each system of equations by a method of your choice: a) 1) 2x −3y =7 2) − + =( y + x 2 9 1) /10 b) 1) y +2x =31 2) 2 y −= x 12 /10 c) 1) 2y + = x 0 3 5 2) 4 x+ =y 2 /10
  • 4. 7. Jack and Isabelle had a combined amount of $210. Jack spent one-third of what he had, and Isabelle one-fifth. The sum of the expenses totaled $64. How much did each of them start out with? /9 8. Cut 25 into two parts, such that the sum of six times one part and eight times the other part is 170. What are the values of the two parts? /9 9. Find two numbers whose difference is 20 and one third of their sum is 40. /9
  • 5. Given the system of inequalities represented below: y 1) x + ≤ y 2 2) − +≥ 2x y − 4 x State whether or not the given ordered pairs are solution-pairs of the system. Answer by yes or no. a) (0, 0) ______________ b) (4, 1) ______________ c) (–1, 1) ______________ d) (0, –2) ______________ /4 10. Draw the graph representing the solution set of the following system of inequalities: y 1) y + x ≤ 3 2) y – 2x ≥ –3 x /8
  • 6. 11. Draw the graph representing the solution set of the following system of inequalities: y 1) y – 2x ≥ 4 2) y <2 x /8