Download MAT096 Lab Sheet 5 - LaGuardia Community College

LAGUARDIA COMMUNITY COLLEGE
Department of Mathematics, Engineering, and Computer Science
MAT96 ELEMENTARY ALGEBRA
ALEKS PILOT
LAB # 5
Name: ____________________________________
Date: ____________________
Instructor: _________________________________
Section: __________________
You need to show all work. Indicate the right answer in the answer sheet. Even if you mark the
right answer, but do not show work on this sheet, you will not be given credit for that question:
Tutor problems are the examples for the unsolved problem(s) that follow them.
1. (Tutor) Find the x value of the solution for the pair of equations:
2x – y = − 9
3x + 2y = 4
a.
b.
c.
d.
e.
Solution: Solving
Substitute
for
for
Therefore,
Spring 2014
2. Find the y value of the solution for the pair of equations:
3x + 2y = 4
x+ y=1
3. (Tutor) Determine the number of solutions the following system of equations has.
4x + y = 13
y = -4x + 11
a. No solution
b. Infinitely many solutions
c. Unique solution
Solution: Rewrite both the equation in the form
False
The statement is false. The system has no solution. It is inconsistent. Hence the answer is a.
Spring 2014
4. Determine the number of solutions the following system of equations has.
2x -3y = 12
x + 2y = -1
5. (Tutor) Solve the system by addition
2x-2y=1
3x+4y=2
Solution: To eliminate x, we multiply the first equation by 3 and the second by -2:
6x-6y=3
-6x-8y=-4
Then we add the two equations and obtain -14y=-1 and y=1/14.
To eliminate y, we multiply by 2 the first equation:
4x-4y=2
3x+4y=2
Adding the two equations gives 7x=4 or x=4/7.
Spring 2014
6. Solve the system by addition.
-2x+5y=1
x-10y=0
Extra Practice Problems (Optional)
1. Find the x value of the solution for the pair of equations:
2x – 3y = 18
3x + 2y = 1
2. Determine the number of solutions the following system of equations has.
6x + 2y = 3
y = -3x + 3/2
Spring 2014
3. Solve the system by substitution.
3x-2y=1
4x-y=0
4. Solve the system by addition.
2x-y=-3
3x-y=2
Spring 2014