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Questions and Answers
Use the graph. Which system of equations is consistent and dependent?
Use the graph. Which system of equations is consistent and dependent?
Fill in the blanks using the available answer choices. Consider the system of equations. 8x + 2y = 8
y = 4x + 4
The system has ______ solution(s).
Fill in the blanks using the available answer choices. Consider the system of equations. 8x + 2y = 8 y = 4x + 4 The system has ______ solution(s).
one
Tristan is selling plastic and wooden picture frames. He sells 7 frames total. The number of plastic frames Tristan sells is 5 less than twice the number of wooden frames. How many of each type of frame does Tristan sell?
wooden frames: [blank]
plastic frames: [blank]
Tristan is selling plastic and wooden picture frames. He sells 7 frames total. The number of plastic frames Tristan sells is 5 less than twice the number of wooden frames. How many of each type of frame does Tristan sell? wooden frames: [blank] plastic frames: [blank]
2 1
Which shows the system of equations that can be entered into a graphing calculator when solving 3.5x + 18 = 5.8x + 30?
Which shows the system of equations that can be entered into a graphing calculator when solving 3.5x + 18 = 5.8x + 30?
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Use a system of equations and a graphing calculator to solve 6.9x + 4.3 = -4.7x + 8. Round to the nearest hundredth, if necessary.
x = [blank]
Use a system of equations and a graphing calculator to solve 6.9x + 4.3 = -4.7x + 8. Round to the nearest hundredth, if necessary. x = [blank]
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Match the correct system of equations to each graph and solution.
Match the correct system of equations to each graph and solution.
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Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
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Consider the system of equations. 3x - 2y = 0
3x + 3y = 33
Which expression could be substituted for y in the first equation find the value of x?
Consider the system of equations. 3x - 2y = 0 3x + 3y = 33 Which expression could be substituted for y in the first equation find the value of x?
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Complementary angles are two angles that have measures with a sum of 90°. Angles P and Q are complementary and the measure of angle P is 6° more than twice the measure of angle Q.
Write a system of equations and use substitution to find the measures of angles P and Q.
[blank]
Complementary angles are two angles that have measures with a sum of 90°. Angles P and Q are complementary and the measure of angle P is 6° more than twice the measure of angle Q. Write a system of equations and use substitution to find the measures of angles P and Q. [blank]
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Solve the system of equations using substitution.
2r - t = 7
r - t = 1
(r, t) = ([blank])
Solve the system of equations using substitution. 2r - t = 7 r - t = 1 (r, t) = ([blank])
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True or false: The system of equation has an infinite number of solutions.
x + 5y = 2
10y = -2x + 4
[blank]
True or false: The system of equation has an infinite number of solutions. x + 5y = 2 10y = -2x + 4 [blank]
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These systems of equations can be solved using elimination by either adding or subtracting the equations. Sort the systems by their appropriate elimination method for finding their solutions.
Elimination Using Addition
[blank]
Elimination Using Subtraction
[blank]
These systems of equations can be solved using elimination by either adding or subtracting the equations. Sort the systems by their appropriate elimination method for finding their solutions. Elimination Using Addition [blank] Elimination Using Subtraction [blank]
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Three times Mary's age added to Beth's age is 34 years. Half of Mary's age minus Beth's age is 1 year. How old are Mary and Beth?
Mary is [blank] years old.
Beth is [blank] years old.
Three times Mary's age added to Beth's age is 34 years. Half of Mary's age minus Beth's age is 1 year. How old are Mary and Beth? Mary is [blank] years old. Beth is [blank] years old.
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A rectangle is x inches wide and 3y inches long. If the length plus twice the width is 12 inches and the length plus the width is 9 inches, what is the length?
A rectangle is x inches wide and 3y inches long. If the length plus twice the width is 12 inches and the length plus the width is 9 inches, what is the length?
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Select all of the ways the system of equations can be solved.
9x - 2y = 4
3x + 8y = -12
Select all of the ways the system of equations can be solved. 9x - 2y = 4 3x + 8y = -12
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It takes 3 hours to paddle a kayak 12 miles downstream and 4 hours for the return trip upstream. Find the rate of the kayak in still water.
Let k = the rate of the kayak in still water and c = the rate of the current.
[blank]
miles per hour.
It takes 3 hours to paddle a kayak 12 miles downstream and 4 hours for the return trip upstream. Find the rate of the kayak in still water. Let k = the rate of the kayak in still water and c = the rate of the current. [blank] miles per hour.
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Solve the system of equations.
2x + 5y = 5
3x + 4y = -3
(x, y) = ([blank])
Solve the system of equations. 2x + 5y = 5 3x + 4y = -3 (x, y) = ([blank])
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Which graph represents the solution of the system of inequalities?
x - y ≥ 2
2x + y > -3
Which graph represents the solution of the system of inequalities? x - y ≥ 2 2x + y > -3
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Fill in the blanks using the available answer choices.
Dana wants to build a rectangular pen for her goats. The length of the pen should be at least 50 feet, and the perimeter of the pen should be no more than 190 feet.
Dana's goat pen could be ______ wide and ______ long.
How many different sets of dimensions are possible for this situation?
Fill in the blanks using the available answer choices. Dana wants to build a rectangular pen for her goats. The length of the pen should be at least 50 feet, and the perimeter of the pen should be no more than 190 feet. Dana's goat pen could be ______ wide and ______ long. How many different sets of dimensions are possible for this situation?
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What is the first step in the process of generating new research questions?
What is the first step in the process of generating new research questions?
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Which type of research question examines the differences between two or more groups?
Which type of research question examines the differences between two or more groups?
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What should be considered to ensure research questions are effectively addressed?
What should be considered to ensure research questions are effectively addressed?
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What is an essential characteristic of descriptive questions?
What is an essential characteristic of descriptive questions?
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Why is it important to review existing literature when generating research questions?
Why is it important to review existing literature when generating research questions?
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What key variable should be defined when formulating research questions?
What key variable should be defined when formulating research questions?
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Which type of question aims to forecast outcomes based on specific variables?
Which type of question aims to forecast outcomes based on specific variables?
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What aspect should be evaluated to ensure research questions are unique and original?
What aspect should be evaluated to ensure research questions are unique and original?
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Study Notes
Module Review (RA1 M7)
- Question 1: Consistent and dependent system of equations is visually represented by overlapping lines on a graph.
- Question 2: The system of equations 8x + 2y = 8 and y = 4x + 4 has infinitely many solutions.
- Question 3: Tristan sells 5 plastic frames and 2 wooden frames.
- Question 4: The system of equations 3.5x + 18 = 5.8x + 30 can be entered into a graphing calculator by rewriting it as y = 3.5x + 18 and y = 5.8x + 30.
- Question 5: The solution to 6.9x + 4.3 = -4.7x + 8, rounded to the nearest hundredth, is x = 0.56.
- Question 6: Matching the correct systems of equations to the graphs and solutions requires analyzing the line slopes and intercepts.
- Question 7: The system of equations shown graphically has one solution. The solution is (2, 7).
- Question 8: The expression 1.5x can be substituted for y in the first equation 3x - 2y = 0 to solve for x in the system 3x - 2y = 0 and 3x + 3y = 33.
- Question 9: Two complementary angles have a sum of 90°. If angle P is 6° more than twice angle Q, the system of equations is P + Q = 90 and P = 2Q + 6. Solving the system gives angle P is 66° and angle Q is 24°.
- Question 10: System 2r - t = 7 and r - t = 1 has the solution (r, t) = (8, 7).
- Question 11: The statement x + 5y = 2 and 10y = -2x + 4 has infinitely many solutions is false.
- Question 12: Different systems of equations are categorized for solving using either the addition or subtraction method of elimination. Examples in the "Answer Bank" are given for each type.
- Question 13: Mary is 16 and Beth is 12 years old.
- Question 14: The length of the rectangle is 6 inches.
- Question 15: The ways to solve the system of equations 9x - 2y = 4 and 3x +8y = −12 include multiplying the second equation by 3, then add the equations. Also, multiply the first equation by 4, then add or subtract equations.
- Question 16: The rate of the kayak in still water is 4 miles per hour.
- Question 17: The solution to the system of equations 2x + 5y = 5 and 3x + 4y = -3 is (x,y) = (-7,3).
- Question 18: The graph representing the solution to the system of inequalities x - y ≥ 2 and 2x + y > −3 displays the area where both inequalities are satisfied.
- Question 19: Dana's goat pen could have dimensions of 29 feet wide and 76 feet long. There are infinitely many possible combinations.
- Question 20: The region where the solution to the system of inequalities -x + 2y ≤ 1 and -x + y ≥ ½ is shaded.
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Description
This quiz covers key concepts related to systems of equations, including their representation on graphs, methods for solving them, and interpreting solutions. The questions challenge students to apply their knowledge of linear equations and graph analysis to find consistent, independent, and dependent systems.
