Elementary Algebra and Solution
1. A line passes through the points (–3, –3) and (–1, 3).
What is the slope of the line that passes through the two points?
Hint X
-3
-1/3
3
1/3
2. A line passes through the points (3, –4) and (7, 12).
What is the y-intercept of the line?
Hint X
(0, 4)
(4, 0)
(0, –16)
(–16, 0)
3. Consider the following system of equations. y = 8x - 8 y - 8x = 7
What can you conclude about the system of equations?
Hint X
The system of equations is inconsistent.
The system of equations is dependent.
The system of equations is independent.
None of these
4. Identify the solution(s) of the system of equations, if any.
-4x - 2y = 12
6y = -12x - 36
Hint X
no solution
(0, -3)
(-3, 0)
infinitely many solutions
5. Identify the solution(s) of the system of equations, if any. x + 5y = 5
4x - 5y = 0
Hint X
(1,5/4 )
(1, 4/5)
(5/4, 1)
(4/5, 1)
6. Identify the solution(s) of the system of equations, if any.
6x + 2y = 8 y = 5 - 5x
Hint X
(2.5, –0.5)
(2.5, 0.5)
(–0.5, 2.5)
(0.5, 2.5)
7. Identify the solution(s) of the system of equations, if any.
7x + 2y = 2
6x - 2y = 6
(13/8, -75/16)
(–4, 15)
(8/13, -15/13)
(8, –27)
Hint X
Hint X
8. A system of inequalities is defined by the following formulas.
251575
1525 75
Which graph represents its solution?
9. Consider the equations:
= -3 - 4 and = 5
Select the solution for .
Hint X
5 3 4
4512080
534
-154
10. Consider the equations:
= -3 -4 and = 5
Select the solution for .
Hint X
5x² + 3x + 4
45x² + 120x + 80
5x² - 3x - 4
-15x² - 4
11. Consider the equations:
= -5 - 2 and = 3
Select the solution for .
Hint X
3x² + 5x + 2
75x² + 60x + 12
3x² - 5x - 2
-15x² - 2
12. Determine the equation of g(x) that results from translating the function f(x) = x2 + 7 upward 9 units.
Hint X
g(x) = (x + 16)2
g(x) = (x + 9)2 + 7
g(x) = x2 - 2
g(x) = x2 + 16
13.
What is the slope of the line that passes through the two points?
Hint X
-3
-1/3
3
1/3
2. A line passes through the points (3, –4) and (7, 12).
What is the y-intercept of the line?
Hint X
(0, 4)
(4, 0)
(0, –16)
(–16, 0)
3. Consider the following system of equations. y = 8x - 8 y - 8x = 7
What can you conclude about the system of equations?
Hint X
The system of equations is inconsistent.
The system of equations is dependent.
The system of equations is independent.
None of these
4. Identify the solution(s) of the system of equations, if any.
-4x - 2y = 12
6y = -12x - 36
Hint X
no solution
(0, -3)
(-3, 0)
infinitely many solutions
5. Identify the solution(s) of the system of equations, if any. x + 5y = 5
4x - 5y = 0
Hint X
(1,5/4 )
(1, 4/5)
(5/4, 1)
(4/5, 1)
6. Identify the solution(s) of the system of equations, if any.
6x + 2y = 8 y = 5 - 5x
Hint X
(2.5, –0.5)
(2.5, 0.5)
(–0.5, 2.5)
(0.5, 2.5)
7. Identify the solution(s) of the system of equations, if any.
7x + 2y = 2
6x - 2y = 6
(13/8, -75/16)
(–4, 15)
(8/13, -15/13)
(8, –27)
Hint X
Hint X
8. A system of inequalities is defined by the following formulas.
251575
1525 75
Which graph represents its solution?
9. Consider the equations:
= -3 - 4 and = 5
Select the solution for .
Hint X
5 3 4
4512080
534
-154
10. Consider the equations:
= -3 -4 and = 5
Select the solution for .
Hint X
5x² + 3x + 4
45x² + 120x + 80
5x² - 3x - 4
-15x² - 4
11. Consider the equations:
= -5 - 2 and = 3
Select the solution for .
Hint X
3x² + 5x + 2
75x² + 60x + 12
3x² - 5x - 2
-15x² - 2
12. Determine the equation of g(x) that results from translating the function f(x) = x2 + 7 upward 9 units.
Hint X
g(x) = (x + 16)2
g(x) = (x + 9)2 + 7
g(x) = x2 - 2
g(x) = x2 + 16
13.