Systems of Equations and Their Solutions

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Which equation completes a system of equations with infinitely many solutions?

3x - 2y = -1

9x - 6y = -6 (correct)

2x - 3y = 1

6x - 9y = -9 (correct)

What coordinate pair is one of the points on the line graphed on the coordinate plane?

(-2, 2)

(0, 3) (correct)

(2, 0)

(-2, -2)

Which equation represents a line that would not result in the same slope as the given graph?

9x - 6y = -6

6x - 9y = -9

4x - 5y = 7 (correct)

2x - 3y = 1

What is a potential solution to a system of equations where one of the equations is 2x - 3y = 1?

(2, 0) Signup and view all the answers

Which of the following pairs shows two points that lie on the same line represented by 2x - 3y = 1?

(0, 3) and (1, 1) Signup and view all the answers

What is the slope of the first equation, $x - 2y = 8$, when rewritten in slope-intercept form?

-2 Signup and view all the answers

Which option accurately represents neither puppy's weight after x weeks equating Semira's and Cedric's puppies?

$y = 0.8x + 12.4$ and $y = 1.2x + 9.2$ Signup and view all the answers

Which of the following statements about the system of equations is true?

The equations intersect at one point. Signup and view all the answers

What is the solution to the equations, $5x + 3y = 18$ and $2x - 3y = 10$?

(2, 1.5) Signup and view all the answers

After how many weeks will Cedric's puppy weigh less than Semira's puppy?

After 5 weeks Signup and view all the answers

What is the approximate solution to the system of equations shown in the graph?

(-2, 2) Signup and view all the answers

What coordinates represent the intersection of the two lines in the graph?

(-2, 2) Signup and view all the answers

Which point does the line passing through (-4, -2) and (2, 2) NOT contain?

(0, 0) Signup and view all the answers

Which of the following equations represents the line that passes through points (-4, -2) and (2, 2)?

y = x + 2 Signup and view all the answers

What characteristic does the line shown in the graph have?

It has a positive slope. Signup and view all the answers

What is the correct solution to the system of equations: 5x + 3y = 18 and 2x - 3y = 10?

(1, 5/2) Signup and view all the answers

Which system of equations should Semira and Cedric use to find when their puppies will weigh the same?

y = 0.8x + 12.4; y = 1.2x + 9.2 Signup and view all the answers

How much does Semira's puppy weigh after 5 weeks?

16.4 pounds Signup and view all the answers

If Cedric's puppy grows at 1.2 pounds per week, what will its weight be after 4 weeks?

13.2 pounds Signup and view all the answers

What is the weight difference between Semira's and Cedric's puppies once they weigh the same?

3.2 pounds Signup and view all the answers

What is the correct system of equations to determine after how many weeks Semira's and Cedric's puppies will weigh the same?

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Which statement regarding the given system of equations is true?

The equations have opposite y-intercepts. Signup and view all the answers

What represents the initial weight of Semira's puppy?

12.4 pounds Signup and view all the answers

What is the weekly growth rate of Cedric's puppy?

1.2 pounds Signup and view all the answers

If $x$ represents time in weeks, what is the weight of Semira's puppy after 5 weeks?

18.4 pounds Signup and view all the answers