9-8 Systems Of Linear And Quadratic Equations

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| By Courtney Frank

Courtney Frank

Community Contributor

Quizzes Created: 44 | Total Attempts: 15,755

Questions: 5 | Attempts: 533 | Updated: Mar 20, 2023

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Questions and Answers

1.

What is the solution of the system of equations shown below?
- A.
  
  (-1, -3) and (-8, -10)
- B.
  
  (0, -2) and (5, 3)
- C.
  
  (2, 0) and (-8, -10)
- D.
  
  (1, -1) and (8, 6)
Correct Answer
D. (1, -1) and (8, 6)

Explanation
The solution of a system of equations is the set of values that satisfy all of the equations in the system. In this case, the given answer (1, -1) and (8, 6) represents two points that satisfy both equations in the system. This means that when the x and y values of these points are plugged into the equations, both equations are true. Therefore, these points are the solution to the system of equations.

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2.

An architect makes a drawing of a parabolic-shaped arch with a linear support intersecting it in two places. The parabola can be modeled by the function . THe line intersects the parabola when x = 2 and x = 4. What is the equation of the line?
- A.
  
  Y = x- 6
- B.
  
  Y = x - 2
- C.
  
  Y = x + 2
- D.
  
  Y = x + 6
Correct Answer
C. Y = x + 2

Explanation
The line intersects the parabola at x = 2 and x = 4. To find the equation of the line, we need to determine the y-intercept. We can substitute the x-coordinate of one of the intersection points into the equation of the parabola to find the corresponding y-coordinate. When x = 2, the equation of the parabola gives y = 2 + 2 = 4. Therefore, the y-intercept is 4. Since the line intersects the y-axis at (0, 2), the slope of the line is 1. Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we have y = x + 2. Hence, the equation of the line is y = x + 2.

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3.

What is the solution of the system of equations shown below?
- A.
  
  (-2, -4) and (-7 and -24)
- B.
  
  (0, 4) and (2, 12)
- C.
  
  (2, 12) and (7, 32)
- D.
  
  (4, 20) and (5, 25)
Correct Answer
C. (2, 12) and (7, 32)

Explanation
The solution of the system of equations is (2, 12) and (7, 32). These points satisfy both equations in the system, meaning that when the x-coordinate is substituted into the first equation and the y-coordinate is substituted into the second equation, both equations are true. Therefore, these points are the solutions to the system of equations.

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4.

Which coordinate is a solution to the following system?
- A.
  
  (4, 14)
- B.
  
  (3, 13
- C.
  
  (2, 12)
- D.
  
  (-3, 7)
Correct Answer
B. (3, 13

Explanation
The given system of coordinates consists of four points. The answer states that (3, 13) is a solution to this system. This means that when we plug in the values of x=3 and y=13 into the equations of the system, they satisfy all the equations.

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5.

Which point is a solution to the system shown?
- A.
  
  (-3, 0)
- B.
  
  (1, -8)
- C.
  
  (3, 0)
- D.
  
  (0, -3)
Correct Answer
A. (-3, 0)

Explanation
The point (-3, 0) is a solution to the system shown because it satisfies both equations in the system.

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Current Version
Mar 20, 2023

Quiz Edited by
ProProfs Editorial Team
Feb 24, 2015

Quiz Created by
Courtney Frank

9-8 Systems Of Linear And Quadratic Equations

What is the solution of the system of equations shown below?

An architect makes a drawing of a parabolic-shaped arch with a linear support intersecting it in two places. The parabola can be modeled by the function . THe line intersects the parabola when x = 2 and x = 4. What is the equation of the line?

What is the solution of the system of equations shown below?

Which coordinate is a solution to the following system?

Which point is a solution to the system shown?