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Multiple Choice: Choose the best answer for each problem.

1.If two lines intersect in a single point, a system consisting of these two linear equations is:

a. dependent b. independent c. inconsistent d.systematic

2. Find the point of intersection of the vertical line through the point (3,-4) and the line whose equation is

3. A movie theater has different ticket prices for those under 12 years of age and those 12 or over. Martha and her two children, ages 6 and 8, paid $15 to gain entrance to the theater. Mr. and Mrs. Sorbet and their 11-year old daughter got in for $19.50. What is the ticket price for those over 12?

a. $5.00 b. $5.90 c. $6.50 d. $8.00

4. A solution (x,y,z)  to a linear system in three variables stands for:


a. the intersection point of three lines c. the intersection point of three planes

b. three points in space d. a point where at two planes meet

5.Which of the following cannot occur if two planes appear in three-dimensional space?

a. They can intersect in a single point.
b. They can intersect in a single line.

c. There can be infinitely many points which satisfy both equations representing the planes.

d. There can be no points which satisfy both equations representing the planes.

6. Solve the system:

a. {(x, 10 – 10x, 8 -7x) | x is any real number}

b. {(x, -4x -7 , 6 -7x) | x is any real number}

c. {(1,0,1)}

d. No solution

7. How many solutions can there be to a system that has one linear equation in two variables and one equation of the form y = ax2 + bx + c?
a. 1 or 2 b. 2 c. 0 d. 0, 1 or 2

8. Solve the system:

a. {(2, 4), (3, 9)}                           c. {(2, 4), (3, 9), (-6, 36), (1, 1)}

b. {(6, 36), (-1, 1)}                        d. This is an inconsistent system.

Ú

9. Solve the system:

10. Decompose into partial fractions:

11. The process of finding partial fractions is used to:

a. rewrite a fraction as its simpler factors.

b. take an irreducible quadratic in the denominator and decompose it.

c. reverse the process of addition of rational expressions.

d. give more practice using systems.

12. The main difference between the graph of a linear equation and the graph of a linear inequality is whether:

a. we have many solutions or only one.    c. we draw a solid or dashed line.

b. we shade a region or not.                      d. we have lines intersecting.

13. Find the maximum value of  P(x,y) = 3x + 2y -1 subject to the constraints:

x ? 0, y ? 0, x + 2y ≤ 6.

a. 4 b. 5 c. 8 d. 17

14. A car company produces two versions of its new model of car, one is the XL and the other is the XL Ltd. It takes 6 hours of construction to produce the XL and 9 hours of construction for the XL Ltd. The finishing takes 3 hours for the XL and 6 hours for the XL Ltd. The company has 90 hours of construction time allotted during a week and 48 hours of finishing time allotted. If the profit on an XL is $2300 and the profit on an XL Ltd. is $3500, how many XL’s and how many XL Ltd.’s should be constructed and finished in one week to maximize profit ?

a. 12 XL’s, 2 XL Ltd.’s c. 10 XL’s, 12 XL Ltd.’s

b. 10 XL’s, 6 XL Ltd.’s d. 15 XL’s, 0 XL Ltd.’s

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