1. Explain what happens when a system of two linear equations is inconsistent. What effect does it have in obtaining a solution? What would the graph of such a system look like?
Choose the correct answer below.
A. When a system of two linear equations is inconsistent, there is no solution. This means that there is no point (x,y) that satisfies both equations. The graph of such a system yields two identical lines.
B. When a system of two linear equations is inconsistent, there is no solution. This means that there is no point (x,y) that satisfies both equations. The graph of such a system yields two perpendicular lines.
C. When a system of two linear equations is inconsistent, there are infinitely many solutions. This means that every point (x,y) satisfies both equations. The graph of such a system yields two identical lines.
D. When a system of two linear equations is inconsistent, there is no solution. This means that there is no point (x,y) that satisfies both equations. The graph of such a system yields two parallel lines.
2. How many possible solutions can a system of two linear equations in two unknowns have?
Select all that apply.
A. Two
B. Three
C. One
D. Four
E. Infinitely many solutions
F. No solution
3. Determine whether the given ordered pair is a solution to the system of equations.
((6/5) 6) 10x+9 - 27-y
5x-3y = 0
Is ((6/5) 6) a solution to the system?
Yes
No
4. Solve the system of equations by graphing. Check your solution.
4x - 3y = 12
6x+ y= -4
Use the graphing tool to graph the system.
Select the correct choice below and fill in any answer boxes present in your choice.
A. The solution to the system is (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
5. Solve the system of equations by graphing. Check your solution.
y = -x+5
x +y = - 3/5
Choose the correct graph of the equations.
Select the correct choice below and fill in any answer boxes present in your choice.
A The solution to the system is. Type an ordered pair.
B. There is an infinite number of solutions.
C. There is no solution.
6. Solve the system of equations by graphing. Check your solution.
y = - 5x + 1
4y + 20x = 4
Use the graphing tool to graph the system.
Select the correct choice below and fill in any answer boxes present in your choice.
A. The solution to this system is (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
7. Solve the system of equations by substitution. The solution set is (Type an ordered pair.)
2x +y = 20
y = 3x
8. Solve the system by substitution.
- x - 9y = -12
y 8x - 23
Select the correct choice below and, if necectgry, fill in the answer box to complete your choice.
A. The solution set. (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
9. Solve the following system by substitution. The solution set is, Simplify your answer. Type an ordered pair.
x 4y +14
x = (4/3)y
10. Solve the system by substitution.
y = 2x
6x - 3y = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is. (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
11. Solve the system by substitution.
x = 6y
5x - 30y = 5
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
12. Find the solution to the system by the addition (elimination) method. Check your answers.
10x + 7y = 21 (1)
5x + 9y = 27 (2)
What is the solution to the system? (Type an ordered pair.)
13. Find the solution to the system by the addition (elimination) method. Check your answers.
5s + 2t = 11 (1)
4s - 6t = 5 (2)
What is the solution to the system? (Type an ordered pair of the form (s,t). Use integers or fractions for any numbers in the expression.)
14. Find the solution to the system by the substitution method. Check your answers.
(1/3)x -(1/12)y = 4
(3/12)x+ (3/5) y =9
What is the solution to the system? (Type an ordered pair.)
15. If possible, solve the system of equations. Use any method. If there is not a unique solution to the system, state a reason.
3x- y = 13 (I)
8x + 3y = 46 (2)
Select the correct choice below and fill in any answer boxes present in your choice.
A. The solution to the system is a. (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
Which of the statements below is a good explanation for the solution?
A. The graphs of the two equations represent the same line.
B. The graphs of the two equations never intersect.
C. The graphs intersect at one point, so the solution is unique.
16. If possible, solve the system of equations. Use any method.
0.2x = 0.1y - 1.5 (1)
2x-y=7 (2)
Select the correct choice below and fill in any answer boxes present in your choice.
A. The solution to the system is. (Type an ordered pair.)
B. There is an infinite number of solutions.
C There is no solution.
Describe the system of equations.
The equations are dependent. Their graphs are identical.
The equations are inconsistent. Their graphs are parallel lines.
The equations are independent and consistent. Their graphs intersect at one point.
17. If possible, solve the system of equations. Use any method. If there is not a unique solution to the system, state a reason.
4x-3y = 5 (1)
- 12x 9y = -15 (2)
Select the correct choice below and fill in any answer boxes present in your choice.
A. The solution to this system is. (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.
Which of the statements below is a good explanation for the solution?
The graphs intersect at one point, so the solution is unique.
The graphs of the two equations never intersect.
The graphs of the two equations represent the same line.