G. Tawfik

1. TEAM WORK

    In a Secondary IV class, teams are formed to work on a History project.
    If there are 5 students on each team, there will be 4 students too many.
    But if there are 6 students per team, there will be 2 students short.

    a. Taking x as the number of teams and y the total number of students, write the system of equations
        that describes this situation.

    b. How many students are there in this class?

    c. How many teams were being formed?
 

2. HOW OLD ARE THEY?

    If we add Christiane's age to Martine's, we get 51 years.
    If Christiane was 6 years older and Martine 3 years younger, they would have the same age.

        a. Write the system of equations to describe this situation.

        b. Determine the age of each girl.

3. What can you say about the two lines whose equation is given below:

    2y - 36 = 6x
    x - y/3 = -12

4. Determine algebraically the solutions of the following systems:

a.   y = 3x² + 2x                                 b.     y² = 4x + 10

5. PARABOLA AND STRAIGHT LINES

On a set of axes the parabola    y = - 3x² + 1    is given, as well as the two straight lines:

                                d₁: y = 2x - 4         and         d₂: y = - 2x + 1

a. Solve graphically the system of line d₁ and the parabola.
 
b. Solve algebraically the system of line d₂ and the parabola.
 

REFLECTION 6  ANSWERS
 

1. 34 students 6 teams   2. Christiane 21, Martine 30 3. The lines are parallel (equal slopes) 4. a.  No solution            b.   (17.75, 9)   (-2.25,  -1) 5. a.  See Graph             b.   (0, 1)    (2/3,  -1/3)    (1, -2)  (-5/3, -22/3)