Testlet 4: Systems of Equations

Which system of linear equations has no solution?

• A. y = 2x – 4, y = –2x + 3

• B. y = (1/2)x + 5, y = 3x + 5

• C. y = (-3/4)x – 2, y = (-6/8)x – 2

• D. y = 5x – 1, y = 5x – 4

A system of linear equations is shown.

y = –2x + 3 y = 3 – 2x

Which statement about the solution to the system of linear equations is true?

• A. The system has one solution because the two equations have different slopes.

• B. The system has no solutions because the two equations have the same slope and the same y-intercept.

• C. The system has no solutions because the two equations have the same slope and different y-intercepts.

• D. The system has infinitely many solutions because the two equations have the same slope and the same y-intercept.

Mrs. Smith wrote the system of linear equations shown.

y = 3x + 4

y = 3x + 7

Which of Mrs. Smith’s students correctly explained the number of solutions for the system of linear equations?

• A. Abby said the system has no solutions because the equations have different slopes.

• B. Bowen said the system has exactly one solution because both equations contain 3x.

• C. Cole said the system has no solutions because the equations have the same slope and different y-intercepts.

• D. Deborah said the system has infinitely many solutions because the equations have the same slope and the same y-intercept.

A system of linear equations is graphed on a coordinate plane. The lines have the same slope but different y-intercepts. How many solutions are there for the system of linear equations?

• no solutions

• one solution

• two solutions

• infinitely many solutions

The graph of a system of linear equations is shown. Which change to line g results in a system of equations with no solution?

• changing the y-intercept of line g to the same y-intercept as line h without changing the slope

• changing the slope of line g to be the same as the slope of line h without changing the y-intercept

• changing the slope of line g to the opposite of the slope of line h without changing the y-intercept

• changing both the slope and y-intercept of line g to be the same as the slope and y-intercept of line h

Which statement best explains the number of solutions to the system of linear equations?

• The system has no solutions because the slopes of the lines are different.

• The system has one solution because the slopes of the lines are different.

• The system has one solution because the y-intercepts of the lines are the same.

• The system has infinitely many solutions because the y-intercepts of the lines are the same.

Select the two systems of linear equations that have infinitely many solutions.

• A. y = 2x + 4 -2x + y = 4

The system of linear equations has (a)   because the slopes of the two lines are ​ ​ (b)   and the y-intercepts are ​ (c)  

• no solutions
• exactly one solution

• infinitely many solutions

• equal
• not equal