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Math 125 Review Ch 2-3
Math 125
Instructor: Yun
Review Ch2-3
1.
Find the slope of the line passing through (3,4), (-2,-2).
2.
Find the slope and y-intercept of the line 3 x  2 y  2 .
3.
Write the equation of the line that satisfies the stated conditions. Express final equations in
standard form.
a. Containing the points (-1,2) and (3,-5)
b. Having a slope of 
3
and a y intercept of 4
7
c. Containing the point (2,5) and parallel to the line x  2 y  4
d. Containing the point (-2,-6) and perpendicular to the line x  2 y  4
e. Horizonal and passing through (-1,6)
4.
Graph each equation. (Label x and y –ints.)
a. y  2 x  5
5.
b. y  
2
x2
3
Graph each inequality.
a. y   3 x  4
b.  x  3 y  6
c. y  
d. 1  x  3 and  2  y  2
6.
8.
1
x2
4
Specify the domain of each function.
a. f ( x ) 
7.
d. x  4
c. 3  y  0
x 3
If f ( x )  x 2  3 x  1 , find
a. f ( 2)
b. g ( x ) 
3
x  4x
2
b. f ( b )
Use the elimination-by-addition method to solve the system.
3 x  2y  6

2x  5y  34
9.
Use the substitution method to solve the system.
5 x  4 y  35

 x  3 y  18
10.
Solve the system
 x  y  4z  29

3 x  2y  z  6
2x  5y  6z  55

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Math 125 Review Ch 2-3
11.
The sum of the measures of the angles of a triangle is 180 . The largest angles is twice the
smallest angle. The sum of the smallest and the largest angle is twice the other angle. Find
the measure of each angle.
12.
Write the system of equations represented by the augmented matrix.
3 4 1


 1 1 0 
13.
Each augmented matrix below has either no solution, infinitely many solutions, or one
solution. Label each augmented matrix with the correct description of its solution.
(You do not need to solve each system. Merely by looking at the numbers, you
should be able to determine the type of solution.)
 1 2 9 3 
a. 0 1 4 7 
0 0 0 0 
 1 3 2 4
b. 0 1 6 0 
0 0 0 2 
1 4 9 6
c. 0 1 3 1
0 0 1 0 
__________________
_________________
________________
14.
A box contains $7.80 in nickels, dimes, and quarters. There are 6 more dimes than
nickels and three times as many quarters as nickels. Find the number of quarters.
15.
Solve the system of three equations using row operations.
Begin by writing an augmented matrix for the system.
At the side of each matrix, make a notation indicating what you are doing.
3 x  y  1

x  y  z  4
 x  2z  3

16.
Solve the system of two equations using Cramer’s Rule.
 x  5y  4

4 x  8 y  5
17. Solve the following system by graphing.
2 x  y  4

 x  2y  2
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